All wallets are generated from the same seed... so the same 24 word mnemonic will enable you to recover ALL wallets that were generated by that mnemonic. This is why you can uninstall and reinstall the coin apps as you like and you won't lose anything... when you reinstall, it will regenerate your wallet again without issue.
So, assuming you put those altcoins on your Nano S AFTER you had restored your Nano seed onto it and created wallets... then yes, you just use "BTC" seed.
That's really good, so I can have a unique seed for all my alt coins.