There are so many wallets out there supporting Erc20 based tokens , in the wallet you have different erc20 tokens with different addresses. Trust wallet supports ethereum based tokens, imtoken, myetherwallet , coinomi, Atomic wallet and alot of others the mobile Apps are on google play store and App store. Go and check them out and download anyone of your choice . I use imtoken.
Point of correction, in a wallet supporting ERC20 tokens, no matter the amount of tokens, all the tokens use one unique ERC20 address. For instance same ETH address copied to receive ETH will be same for any ERC20 token like BZRX or USDT (ERC20 version). So in essence you just need your main ETH address to receive any other erc20 token in that wallet and not otherwise.