Your RD likely doesn’t have the rated capacity for more chain wrap or cog size. Instead look at the crankset. You can swap it for a 22-32-42 or similar. You don’t need to change the shifters or derailleurs and you’ll only need to scoot down and adjust the front derailleur. That’s what mountain bikes came with for years anyhow. The bigger rings only really make sense in city commuting mode, that’s why it’s usually seen on hybrids.

edit: tyrion’s idea works if the chain is not too loose in small-small or you avoid going there. Minimum price.