It sounds like a fun project and I'd never discourage that. But whether you can do it without spending a lot of money really depends on how much you have budgeted.
What I do for things like this is to make a planning list of parts required, or possibly/probably required. Most expensive down to least. You'll soon get an idea of whether your budget fits.
Probably you will find that the shifters are top of the list.
Then the chainset/chainrings if you need to. As far as I understand (and I could be wrong) the inner dimensions of an 11s chain are the same as a 10s chain so if your chain rings are not worn out you don't necessarily need to replace them. But if they are worn and you're fitting a new cassette and chain and starting afresh with new shiny stuff then replacement rings at least - maybe a whole crankset - may be on the cards. Price up all the options.
Next things on the list will be mech(s), cassette and possible freehub/wheel costs.
Don't forget cables, bar tape, chain and any new special tools that you might need.
I fitted (well, actually I paid the LBS to do it) new R7000 11 speed last year. This was a replacement rather than an upgrade as my existing drivetrain was completely shot - many broken and worn out bits. I chose R7000 for various reasons, but the fact that it has an extra gear was incidental, it wasn't really a factor.
The result was (and is) excellent but the fact that it has an extra gear is neither here nor there. If you were to use sneaky magic to revert the number of gears to the 10 I had before, but leaving everything else the same, I doubt if I'd notice.
