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Holding coins on multiple chains should be fine, but Ledger Live may interact with them differently. For example…i have AVAX on my Ledger but I cant really interact with it in Ledger Live ( last time I checked ) but I can still use my Ledger to keep it safe. I integrate my Ledger into Avalanche wallet on their website where i can interact with it in a very cool way that lets me use chain-c, chain-p and chain-x.
In this instance, Ledger Live is already restricted but still a very useful tool in limiting the transactions of my AVAX wallet, it must have the physical confirmation of my Ledger for any withdrawals