From my experimentation it looks to me like the furthest maximum meaningful verbosity in Valgrind's Memcheck is two --verbose flags1.
Is that true?
1: Three or more `--verbose` flags would be allowed, but I think they make no substantial change in the output.
You can give as many -v options as your want.
Most of the verbosity usage are comparing with verbosity 1 or 2, but there are a number of comparisons with verbosity 3. I found no code checking verbosity 4 or above.