amiibo aren't a memory card. They're something different with a little bit of memory
Also, you can go for many without deleting it.
Take my Link amiibo. I can use it on Smash Bros, Hyrule Warriors, Style Savvy 3, ACE COMBAT™ ASSAULT HORIZON LEGACY +, amiibo Tap & Play, Captain Toad, Mario Kart 8, Mario Party 10, One Piece Super Grand Battle X and Yoshi's Woolly World, with more on the way, all without having to delete my data.
You meant to ask how many games can save data to an amiibo, which is obviously one at a time and they do need to add a bit of backup software so you can juggle where necessary due to constraints in NFC chips (not Nintendo being stupid, that's how NFC chips are. Deal with it)