Yes, you can do that. If the offshoots get a little large you can pinch them off and use those for new starts too. Actually you should be able to do that now but put the little offshoots into a covered container with perlite. Keep moist and covered until rooted and growing.

Thanks! A friend gave this to me and the mother plant has been in their family for about 50 years. I want to do him justice. For pics, see http://gallery.me.com/fotosbyfred#100652