More switching like that can be done. But you might do better by making more use of the buck characteristic of the output inverter stage.
How do you mean?
A traditional output H Bridge stage uses 4 switches, and can deliver a modulation index
d between +1 and -1, i.e. 100% duty cycle +ve and 100% duty cycle -ve. Over moderate time scales (e.g. 0.5 - 1ms) we can average this to estimate the output voltage
v_o.
v_o = d v_dcWhere
v_dc is the DC bus voltage. This means that
v_o will always be less than or equal to
v_dc, which is what I meant by 'buck characteristic.' Sorry if that was a bit abstruse. It means that while you might only need 170 V DC to get a 120 V AC output, you can operate that same converter at 300 V DC (but efficiency will drop a little). So that offers a degree of freedom to your design.
As an aside,
d changes with time to make the sine wave, for example:
d = D * cos (\omega t)Where
D\ is often called the modulation index and sets the AC output voltage magnitude (actual control systems vary a lot).
D_peak can be between 0 and 1.
Chaining many stages on the LV side can wreck efficiency
What if you don't use a plain diode, but rather a mosfet?
That's a good question. Certainly, using synchronous rectifiers can help with
conduction losses - especially for low voltages. However, there are also
switching losses to think about. If you put down a big MOSFET, it will have lots of capacitance, take longer to switch on and off, and dissipate more energy while it does so.
When considering overall efficiency, consider the following argument. You could do three stages (first image) carefully and hit 98% each. Overall efficiency around 94%.
Or, you could do two stages and make some compromises to the DC DC stage to achieve wide input range with 96% efficiency. The inverter retains 98% efficiency. Overall efficiency around 94%, but you've used less components (so smaller, cheaper, less to go wrong).
Hope this helps.
EDIT: fixed quote format problem.