Can a directory belong to more than one group?

If your filesystem supports posix acl extensions, then yes you can have more than one group. Most normal unix/linux tools and programs wont show you more than the default user:group:other stuff.

Use getfacl <file/dir> to get current acl settings and setfacl to set them.

$ getfacl .
# file: .
# owner: root
# group: src
user::rwx
group::r-x
mask::rwx
other::---

 # only user root got write access and src group read/exec access
$setfacl -m g:root:rwx .
$setfacl -m g:staff:rwx .
 # and now root and staff groups have full write access

$ getfacl .
# file: .
# owner: root
# group: src
user::rwx
group::r-x
group:root:rwx
group:staff:rwx
mask::rwx
other::---

See man mount for mount options

  ext2:
  acl|noacl
          Support POSIX Access Control Lists (or not).

See man getfacl and man setfacl for acl examples and options.