How can I have more than 16 groups per user?

The number of groups per user can be increased to at most 32:

set ngroups_max = 32

This setting may give rise to NFS interoperability problems, as
typical NFS servers only support 16 groups when using AUTH_SYS/AUTH_UNIX.

The other NFS authentication mechanisms map "netids" to usernames
on the servers and can support more than 16 groups.
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