Mention of on-line/offline play has suggested something to me. Perhaps there could be a method of synchronising between games on different devices? For instance, you could play the game on the computer then pick it up again on your smartphone. I appreciate that this would probably only work between devices from the same maker, so might only apply to someone with a Mac desktop/laptop and an iPhone or iPad, or perhaps between Android tablets and smartphones (or even two smartphones).

Obviously it would have to be an option to synchronise, so people could have two (or more) different families on different devices if they wished.