Though you are limited to 10 slots, you can still use the 'Merge Plugins' program (available on Nexus) to combine a lot of similar mods, giving the possibility for far more than 10 mods. Please note that 4 of the slots will be taken up by the Skyrim DLC and the Link outfit, but these can be overwritten as they load automatically from the game. There is a Youtube video called ' Skyrim PC Mods on the Nintendo Switch' that will take you through all of the steps to get mods running. That is beyond the scope of this post, but you can find all of the info you need online.
You will obviously need a Switch running custom firmware. This is not a comprehensive list, but rather a collection of the ones I've tried personally. I know the Switch modding scene isn't big here yet, but for those who are interested, I wanted to share some tips and make a list of the mods that I've personally found to work thus far.