You can install up to 18 apps (depending on which ones you install).
If you install an app which crypto is a clone of Bitcoin[1], there will be more space left because they share the same library - hosted in the Bitcoin app - so their size will be lower. However, for apps that use its own library (like Bitcoin, Ethereum, Ripple, FIDO U2F and Password Manager), the space taken will be bigger, so you can only install from 4 to 5 apps "bigger" apps.
Keep in mind that when you delete an app, you will not lose your coins. So you can install it back later and keep using like nothing had happened. E.g: you install the ETH app, receive some tokens but want to install the NEO app. So you delete the ETH app, install the NEO and receive your NEO coins. Then, you want to manage your ETH again, so you delete the NEO app and reinstall the ETH app. Your ETH tokens will still be there.
[1] which are: Bitcoin, Bitcoin Cash, Bitcoin Gold, Litecoin, Dogecoin, Dash, Zcash, Komodo, Stratis, Posw, Pivx, Viacoin, Vertcoin, Stealthcoin, Digibyte, Qtum, Hcash
Reference:
https://support.ledgerwallet.com/hc/en-us/articles/360003117594