Don't even need a new game. You could clone pokemon by turning the game off mid-trade. My school had a kid that got a Mew from an event, then cloned it for everyone who wanted one.
It became possible in GSC to clone with a single cart. Switch boxes and time a restart correctly during the save and bingo bango, you have a cloned pokemon with whatever item it was holding.
This was awesome for getting extra Master Balls and Rare Candies.
I think many people figured out the Missingno shoreline kept some form of "last encounter table" in it, so I wouldn't be surprised some people may have tried to go there right after Mewtwo to chance themselves at more.
Unfortunately we do have that info nowadays, and we know that doesn't work.
this was basically me for a while, had a team that was all deoxys forms named after 4 of the spice girls + two Arceus named after the last spice girl and Barack Obama
The trick was to clone Mewtwo in a later Pokemon game, trade that to a "middle man" Pokemon game that was compatible with Red and Blue, and BOOM all Mewtwo gang!