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Does the nano ledger support many different coins?

Yes, go to their website to see the list of coins supported at the moment.

Yes. Even better than the Ledger Nano is Ledger Nano S. Nano S allows you to add additional coins beyond the default btc, eth. But not a ton, just maybe 4 or 5 more with the version I bought last month. You use the Ledger Manager app from Chrome to add coins to your Nano S.

Alternatively, or perhaps additionally, Nano S is compatible with myetherwallet, though I haven't used that option.