There are a few tubes that are suitable replacements for a 12AX7. That would be 5751, and 12AT7. I would not go beyond 30% to 40% below nominal gain.
Typical gain factors of 12 series preamp tubes
12AX7 being 100 (nominal)
5751 is 70 (30% reduction)
12AT7 is 60 (40% reduction)
12AY7 is 45 (55% reduction)
12AV7 is 41 (59% reduction)
12AU7 is 19 (81% reduction)
Dropping too low will not be all that great. Typical replacement strategy does have limits. Say for example you have a Mark Series amp where the reverb send and return are split between two different tubes and the other triodes are used for gain stages. Dropping from a 12AX7 to a 12AT7 is okay and will alter gain structure and tone.