You could pack upper and lowercase roman letters and numerals for a total of 62 characters and then have room for a period and space and you’re full. With only uppercase you can a decent set of symbols, see the SIXBIT encoding
https://rabbit.eng.miami.edu/info/decchars.html
that Digital used for file names back when there was a computer industry on the US East Coast. If you wanted something general purpose you’d need to add some kind of shift to get lower case characters if not additional symbols and control characters, but now the meaning of the characters depends on state which might have been seen as a burden on the peripherals of the day and is certainly more of a hassle to program. Note it was seen as decisive that IBM’s 360 used 8-bit characters that could have fit the ASCII code but they went with the 8-bit
https://en.wikipedia.org/wiki/EBCDIC
code instead because it was easier to make compatible with older keypunch machines.
Already 8-bit is looking like overkill, I think the control characters were not really properly utilized in 7-bits, 8-bits let you fit some combination of extra symbols, modified roman letters used in other european languages, and such. You can’t cover every European language in 8 bits (which is why they had different code pages) but you could get most latin variants and probably some other sets like Greek, Cyrillic, even Japanese Kana, in 10-bits but hardly anyone wants to use all those characters at the same time.
If you had a sixty bit computer you might also consider a 5-bit code set like