Well outside of organised league cricket, if there is an appetite for more, why not arrange friendlies with other clubs?
Alos sounds like your leagues must be quite small.
My division has 12 teams, and we play each other twice, home & away, so there are 22 league matches.
Plus a league cup
Plus a county cup
Plus a national cup
Plus a 20/20 cup (which has qualifiying groups, so it guarantees another handful of fixtures)
Plus any friendly fixtures.
If there's not enough cricket there surely the club members should put more pressue on the leagues to organise bigger and/or more competitions.