replacing 1 large boiler with 2 smaller ones

It sounds like you have a control and/or zoning problem, rather than a boiler capacity problem. If you replace one large boiler with two both plumbed to the same system that serves both apartments in common, this will not solve your issue.

If you install a separate boiler for each apartment as its own zone,with its own thermostat, that should fix it.

Beyond the boiler, how are the radiators piped?

As @bburd said, this is a controls problem not a boiler problem. If you existing boiler is in good shape, there is no reason to replace it.

You need outdoor reset control with boiler protection. This will adjust the heating loop temperature based on building load so people won't overheat in the shoulder season. Bonus is it prevents banging and clanging from pipe expansion as the heating loop temperature is kept even. Even bigger bonus, lets you run your boiler at lower temperature a good part of the heating season which saves fuel costs.

https://www.contractormag.com/hydronics/article/21155243/look-like-a-pro-with-reset-control

Since there is less than 450,000 BTUh net going to the building system, the mixing valve will be a 2” three way valve This valve needs a motor to automatically open and close the valve as needed to maintain the mix temperature to the radiator system The motor for this valve is a Tekmar 743.  In order for the valve to know what position will deliver the proper system temperature and also protect the boiler from low temperature return water I specify the  Tekmar 360 to operate the mixing valve 

As I said before, that 360 can operate a single boiler, but in your case we will be sending the call for heat to the boiler to a Staging control. Tekmar 275 can handle 2, 3 or 4 boilers and will also operate the boiler(s) at a reduced temperature with a minimum return water temperature.  So you have 2 ODR controls.  One for the boilers that will not go below  a 130° return water temperature. And the other to reduce that temperature to the radiators in order to keep them from overheating when the minimum boiler temperature is too high.

This may take some time to design the whole thing so look for my design in a few days.   Here are the links to the Tekmar parts.   It took me a year to understand the illustrations and how to actually connect the wires, back over 30 years ago.  But once I understood them, I have been able to make easy to follow wiring diagrams for others to follow.  

• Here are the links to the Tekmar parts so you can begin to source them.  https://www.supplyhouse.com/Tekmar-724-2-Brass-4-Way-Mixing-Valve-4873000-p
• https://www.supplyhouse.com/Tekmar-743-Actuating-Motor-for-34-Way-Mixing-Valves
• https://www.supplyhouse.com/Tekmar-360-Floating-Action-Mixing-Control-4173000-p
• https://s3.amazonaws.com/s3.supplyhouse.com/product_files/275%20install.pdf.
• the replacement for this control is the Tekmar 294 if the 275 is no longer available
• https://www.supplyhouse.com/Tekmar-294-TEKMAR-Boiler-Control-One-tN4-Four-Stage-Boiler-DHW-Setpoint

Do not purchase anything until others critique my diagram and piping design. @hot_rod and others may have a less expensive ideas.  But some are all going to push the ModCon boilers that have this stuff built in.  That is what I would do in your situation. But that's me.

This would be your piping diagram according to Tekmar. All 2" copper, except where the individual boilers are connected in 1" copper to the 2" shared piping. The 2" 4 way valve will add the boiler protection needed for the return piping BUT having the Boiler mixing valve to ensure the return gets up to 130° ASAP, won't hurt. I like. the Califfi 280165A valve set at 130°.

Click on the picture to zoom in for details

The basic wiring logic is on the piping diagram however the nitty gritty diagram with all the terminal numbers is a little more involved. I just wanted to post this to see if there are nay other ideas out there. I did not include the fill valve location however I believe it is best located on the 2" common pipe just before the P1 circulator and the temperature sensor probe. The CST on the diagram are Closely Spaced Tees not to exceed 12" about 6" should be just right

@Kaos , I believe you missed a few posts here. @dronic123 has a single boiler in a 100 year old multi family building, that is showing signs of a leak. To me, that means it is time for a replacement. The management wants to stick with cast iron atmospheric. They are simple to work on. That way, in-house staff can do most of the repair work. The original query was to use 2 boilers of different sizes to equal 300K NET. Load calc already completed. The old boiler is 500K NET. The multi-stage new to equal 300K NET

There is no existing control system that will stage a small boiler then large boiler then both boilers to get three different firing rates. So I suggested three small boilers to make three stages of boiler input. Tekmar already has that control system, so no reinventing the wheel.

The problem that @dronic123 wants to solve with this 3 boiler design is to keep the system from overheating the apartments. I believe, as do others, that the overheating will not be solved by the staging of boilers alone.  There are over 40 radiators in the building so TRVs can get costly. Outdoor reset is a better option IMHO. So I thought a Tekmar 360 to control a 4 way valve, and a Tekmar 275 would be the perfect match up. But I came to find that some of the suppliers have discontinued offering that control in favor of the newer Tekmar 294 staging control. 

Now that you are up to speed, I was looking for other options to do three cast iron boilers and offer ODR to the radiators.   I have offered injection pumping systems in the past but never actually installed one.  I did have one oil burner client that has the 4 way valve for their ODR system and remember that they were very satisfied with it.  

Just looking for suggestions to connect an old gravity radiator system that was converted to a forced hot water system using one boiler 20 or 30 years ago.   That system is overheating the place and I have this as a starting point for others to comment.   Any thoughts?    

Assuming the OP is somewhere in the north west, say 6000 HDD days with a 5F design temp.

If we start with 300kBTU/h that would put the place at 5kBTU/h per heat degree.

So in a year would need about:

6000*24*5000=7200 Therms of heat.

Assuming this is supplied by an 80% boiler, that is about 9000Therms/heating season. So if the OP uses about that much than 300k is correct. My guess based on similar place in colder climate (1907 12 plex with no insulation), the number is about 1/2 that.

No need to guess boiler size, calculate. A single right boiler with outdoor reset will be a heck of a lot cheaper install.

How I approach these is:

1. Get a realistic design heat load. I usually work back from the historical fuel usage to get this number.
2. Typical winter design heat loads only require 60% capacity for about 90% of the heating system.
3. I use this as the design target for the first stage boiler.
4. You will usually also find that this capacity is about what you need for freeze protection is you are down to a single boiler when at peak design conditions ( Hold the building about 45F at 0F, in my area, Chicago)
5. Install a first stage boiler with this capacity, often leaving the original boiler for use only a couple days a year during the extreme temperatures

or

Install 2 boilers each at 60% of design load for full back up.

7. Set up the boilers with return temperature protection piped in paralell with each other, but P/S to the system main. If doing full outdoor reset of the system, use return mixing valves (i.e. Esbe) or if doing partial outdoor reset, manually set bypass on the boiler. This really depends on the peak operating temperature of the system. If you really need 180F water at design ( extremely rare) then mixing valves probably will be needed. However, if the design temp of the system is much lower, a manual bypass is often all that is needed.

For example, my church has a 1950's steel pipe in concrete slab radiant system. Design supply temperature for the system is very low ( well under 100F, especially with the added insulation and new windows), so I use a fixed bypass on the boiler, with the boiler piped P/S to the system loop. The bypass sends nearly 100% of the supply water back into the boiler and only a small amount out to the main system loop. Since almost all the supply goes back to the return, the boiler warms up very quickly and then as it gets up to temperature, the delta tee between the boiler loop gets high enough to start transferring significant heat to the system loop. The boiler generally will be running about 180F, while the system loop is about 80F.

I wouldn't worry too much about the losses that may occur when on the edge of the capacity of the first boiler and need to bring on the second stage( like on cold nights) because the btu stored in most package gas fired cast iron boilers are quite low. For a 150,000 btu model its only about 1.5 to 2.5 gallons of water and 350 pound of cast iron, which only hold about 1/10 the btu per pound of water. Using a 2 gallon boiler at 350 pounds of cast iron, that's about 52 btu's/degreeF to change the boiler temperature.

With a well sized 2 stage atmospheric gas cast iron heating plant with outdoor reset, fuel savings over a previous typical single oversized atmospheric cast iron boiler installation typically run 30 % or more. This savings level and the simplicity and long life of cast iron atmospherics is why I don't think condensing boilers are worthwhile in applications where staged boilers can be used.

Partial outdoor reset is resetting the supply water temperature down to the lower limit the cast iron boilers can operate at continuously. This is typically about 130F for small package atmospherics ( 110-115F return) , but there are commercial boilers that can go down to about 90-100F. Full outdoor reset would be resetting water temperature right down to the room temperature in warm weather. Most older systems, particularly radiators, don't need supply temperatures above 140F at design, so partial reset is often useless unless the system is zoned. This particularly holds true for multi-unit buildings because the internal heat gains tend to be quite high along with the heat loss being relatively low per sq ft of space. Here in Chicago, the old 1880 to 1940 3-story brick multiunit buildings usually only need about 15 to 20 btu/ sq ft at 0F outdoor. You have to remember the system is sized to heat the building assuming there are no internal gains and the sun never shines… so way too big for typical usage of residential buildings.

To pipe the boilers in parallel, the supplies are joined together before reaching the supply tee and returns are joined together before reaching the return tee (P/S tees). A check valve is installed on each boiler supply where they join together. This piping arrangement keeps the return temperature to each boiler the same, which can be important if the system has to run at high supply temperatures.

For the mixing valves, we have used return mounted ESBE thermostatic valves for these little boilers and just follow the manufacturer's instructions.

In your original diagram, the boiler pump is hydraulically separated from the system by the closely spaced tees. Likewise each boiler pump is separated from each other by the closely spaced tees.  And the system pump is hydraulically separated from the boiler pumps by the closely spaced tees. 

The closely spaced tees are at the arrows that say "Webstone CCT Purge". You actually got that right. Good design. But there is a better design. Here is a video that indicates that better design. (around time stamp 46:40)

piped in parallel they all see the same return temperature as SW mentioned, I prefer that with non condensing boilers, compared to the close tee method where temperatures are different at each set of tees

You will need to include Flo-Check valves and I added the indirect. if you use 1-1/4" piping that you can operate 2 boilers for faster recovery. If you use 1" then you only need to operate one boiler and the Tekmar will figure that out for you with the proper settings.