With my 10-speed bikes on a planned tour through the high sierras I replaced the largest cog that was a 24 tooth one with a 28 tooth cog so I had in effect a "granny" gear for the grades. If not racing all that matters is being able to go up the longest and steepest grade without having to dismount. 10 speeds and 1 of them an ultra low speed was plenty good enough over thousands of miles with touring gear on the bike.

My Trek 5200 has "only" a 9-cog rear cassette that is a 12-25t and with 53/39 chainrings in the front there is nothing I cannot manage on the road, but if I did my first move would be to a 12-32t or 12-34t cassette. No need to fool with the chainrings, although I have gone to much smaller outer chainring at 53t which replaced a 60t chainring. With the 12-60 I could pedal downhill and get to speeds that were on the edge but when one is young and fearless (foolish) I did things I would not dream of doing in my later years when the body takes longer to heal from injuries.