Can I use a step up transformer?

Please let me know, if for example: I own an active high gain PS designed for MC cartridges with at least an output of 0.3mv and things are that I own a cartridge with a lower output ( say: 0.20mv. ) that I really can't use it with.

Maybe you should pick a better example. The 0.2mV cart. will only be 3.5dB down from one with 0.3mV output. This should be well with-in any system capability to compensate with the volume control. I doubt that the 3.5dB increase in noise would be noticed. E.g. I recently assembled a phono pre for a customer that was MM input only. My TT has a cart. installed with an output of 0.4mV. To test the unit I ran my low output cart. into its MM input. Other than some extra noise noticeable when the music was not playing, it was an enjoyable listening experience. BTW, the MM unit I was testing was a tube design.

3.5dbs means that the PLP needs to double the power and if the PLP was designed for at least 0.3mv output cartridges then its specs/overall characteristics could change in dramatic way.

We're talking voltage gain here, not power. If a phono pre is designed to handle 0.3mV cart. it will handle a 0.2mV cart. just fine. The only "cost" is a 3.5dB loss of S/N ratio when one supplies the extra 3.5dB of gain with the following line stage using the volume control. The phono pre does not have to double its power. Now if that extra noise is enough to kill a quality listening experience for you then you are entitled to your opinion.

As far as changing "characteristics" (its not clear what you are referring to here), if this were the case then your theoretical phono pre designed for 0.3mV cart. would not be able to play quiet passages without changing its overall characteristics. Presumably it should be able to handle from 0.0mV - well over 0.3mV so why should a cart. with less output change its "characteristics"? Like I mentioned, I played a 0.4mv cart. on a MM phono pre designed for 4.0mV cart., a 20dB difference. Other than the extra noise, no other changes.

BTW, I have read the whole tread and some of the posters here remind me of medieval clerics sitting around arguing over how many angels will fit on the head of a pin.