Let's say we have total supply of a token set at 10,000,000. There are 9,999,999 tokens at the moment. What if at the same time a token is minted on both Polygon and Ethereum?
I am in a project that originated on BSC and then expanded to Polygon. The project tokens can only be minted on the original BSC chain. The only way they exist on the Polygon chain is via a BSC - Polygon bridge, hence, the total supply is intact.
However, it's also possible that the project can decide to mint tokens on both chains, thereby increasing the original total supply of the Project (usually they would give the Polygon token the prefix p). It's at the discretion of the project.