My understanding is that transformers are rated in Volt-Amps. Typically the 120/24 VAC transformer in a boiler or furnace is 40 VA.

I understand that to mean that if the low voltage side of the transformer is 24 volts AC, the maximum low voltage amperage will be 40 VA divided by 24 volts, or 1.67 amps. And, the high voltage current will be exactly the same VA (because energy can neither be created nor destroyed), so the amperage on the high voltage side would be 40 VA divided by 120 VAC, or 1/3 of an amp.

Is that not correct?

Should the OP then not be looking for a higher VA transformer?

Also, my understanding is that if transformers are the same VA rating, they can be connected in parallel so that two 40 VA transformers wired in parallel will provide 80 VA of power, and that's generally sufficient to power even the most power hungry kinds of door bells or chimes since only one button typically gets pushed at a time.