Not sure what you mean by ‘compatible’ in this context. But yes, you can have as many different ERC-20 tokens on the same address as you like. Technically that would just be different token inputs with the same target address written to the chain.
An ERC-20 token is always created by a smart contract, so each different ERC-20 token has a different originating smart contract which identifies the token.
ERC-20 are fungible tokens, so eg. If you have 20 UET (Useless Ethereum Token) then all these 20 tokens are the same, not possible to identify each single of those 20 tokens.
In difference, Ethereum tokens of the ERC-721 standard are non-fungible tokens aka NFT (eg like Cryptokitties), where each token originating from the same smart contract, has an identifying number. That makes it possible to identify a single token within all tokens from the same origin. Eg. To have a Cryptokitty nr 999 which is unique and different from nr 998 etc.