Have a look at voltage doublers:
https://duckduckgo.com/?q=psu+"voltage+doubler"&iax=images&ia=imagesThe principle is quite simple.
For SMPS power supllies on 230Vac the input is a simple full bridge which rectifies to about 310Vdc.
Then there are 2 small modifications to have it run on 120Vac.
First the elco is split in 2 elco's in series.
Then the center tap between the elco's is shorted to one of the input terminals.
This means the top elco is rectified to around +150Vdc, and the bottom elco is rectified to around -150Vdc, and together they are 300V, about the same as from the full bridge.
Additonal advantage is that 200V elco's can be used instead of 400V elco's, Disadvantage is that somewhat bigger elco's must be used because of the (2x) half wave rectification for 120Vac.
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With smaller power supplies it's more common that they simply accept a wide change of input volatage.
With a bit of forethought it's not too difficult to design an SMPS for which the input voltage can have a 1:4 ratio.
If you have a look at the very common small smps modules from Ali / Ebay / China with for example a LM2596 or MP1485, they have a wide input voltage, and they simply adjust the PWM duty cycle internally to regulate the output voltage.