Do you can give us detail information about the 10 altcoins ? Of course it is possible to keep their in same wallet
if your altcoins be supported by the provider of wallets,
Saving altcoins on the exchangers is something dangerous for your coins due to the exchangers can be shutdown like BTC-e
it was gone and many more exchangers was gone. You must try to use the altcoins wallet to keep them, here for the candidate of wallets https://steemit.com/cryptocurrency/@mrilevi/the-top-5-best-altcoin-wallets-an-overview choose the best for you.