Older inverters used a milti tapped transformer to do what your asking for. (early switech?)

Problem the transformers require an activation energy, only a few percent and an efficiency hit.

My APC 3kw, it's sin out, uses a transformer for AVR and inverting. No load it draws 47watts. The transformer gets warm, room at 73'F, transformer is 115'F. Quick idea is most of the 47 watts is in the transformer.

Your piece price for parts is 4x higher than a huge OEM. Even with their markups you end up paying about the same for the parts as a complete working unit. Engineering is free!-) OK, not always.

I would like to remove the transformer from the circuit unless its needed, would save most of the 47 w.
To make the unit more efficient use several transformers, 100w, 500w, 1500w, 3kw...
Use one or more transformers as the conditions require.

New units do not use a 60hz transformer. High frequency simulated sin wave. Efficiency is much higher. Very complex to design.

I bought four 3kw UPS to back up my house. I only installed one unit to keep the batteries and back up my 15 SETI computers. (Off line for the summer due to AC cost) Not liking the 200watts running current the UPS uses. Bought several broken UPS: 5kw, 2kw, 1kw to modify to switch the transformer in/out as needed. Not got that far. Don't expect I ever will.

I plan to build a zero energy house in the next year. The inverter will be one of the newer grid tied inverters and pay the $2000.