Yes it will work. Harris Cyclery/Sheldon Brown has done this expensively for 9 speed cassettes, but I am unaware of many people doing it for 11 speed cassettes. I believe the thought is that with 11 cog the steps are so small you don't need to do custom. But no reason why you have to ride what the manufacturers want.

Theoretically you could just replace single cogs. For example you could buy a Shimano 12T cog designed for the 1st position (includes integrated spacer) and 1 tooth change to the next larger cog (13T). Ideally you would change the current 14T cog, which is designed for a 2 tooth change to the next larger cog, with a 14T cog designed for a 1 tooth change. You would also need a 15T cog designed for a 1 tooth change to the next larger (16T) cog. Unfortunately the larger cogs (14T, 15T) are not available individually unless you found someone disassembling a cassette and selling them individually.

Good luck finding that perfect gearing. Just be careful, chasing that dream can lead you down a rabbit hole.