It’s a common practice in consumer electrical devices to chain multiple batteries together to get more power. So it stands to reason that you could chain multiple small American Flyer/Lionel/Marx transformers together to get more power.
It doesn’t work that way–you can’t chain two 90w transformers together to get 180 watts. But there are still reasons you might want to use multiple transformers; say, to control different blocks of track on your electric train layout.
The first thing you have to do is make sure your transformers are in phase–that is, their polarities are synchronized.
Connect post A to post A (or equivalent to equivalent), then connect a wire to post U (or base, on Flyer transformers) on one and leave it loose on the other end. Turn both transformers up to around 18 volts. Touch the loose wire to post U on the other transformer. If you see a big spark, they are out of phase. If you only see a small spark or no spark, they are phased.
If the transformers are out of phase, unplug one of them, turn the plug 180 degrees, and plug it back in. Then repeat the test.
To keep them in phase, plug both transformers into an extension cord or power strip. Mark the top of the plug with a dot of paint. As long as both transformers are plugged in the same way, they will remain in phase.
Next, divide your track into blocks. Insert an insulating pin in the center rail (Lionel) or whatever rail isn’t connected to the base post (American Flyer) on each end of your block. Now you can power this block with a different transformer.
There are two reasons to want to do this. Perhaps you want two loops, with a separate throttle. Another good use is with a section of elevated track. You may want extra voltage on the upward leg of the elevation; you’ll certainly want less voltage on the downward leg. By isolating the upward and downward legs on their own blocks, you can power them with separate transformers, each with the throttle set appropriately.
When you wire your transformers, connect all of the U or base posts together. Then run the A post from each transformer to lockons on the appropriate block. The A post connects to post 1 on Lionel lockons, or the unlabeled post on Flyer. Connect post #2 on your lockons to whichever U/base post is closest.
Rather than steal precious wattage from the trains, you can power your accessories with a cheap starter transformer. These transformers range from 25-40 watts and many people outgrow them quickly, so they’re cheap. Strictly speaking, you don’t need to phase the power for these, but you can save wire if you do. By phasing them, you can grab the common post off the nearest convenient track section, rather than running two wires all the way back to the transformer.