It is possible and you will find wallets that support multiple cryptocurrencies but none of them will ever support each one of them because there is a lack of interest. A wallet provider wouldn't waste resources to develop something that is not going to be used.
If this is possible so what wallet would you suggest to store many of altcoin in one web wallet?
As far as i know, i never find any wallet which can be used for storing many of altcoin.