Already with many providers of such solutions, so the question is if the market can carry more.
As is typical for app-centric services, there’s of course also a back-office service handling the communication between phones and keeping track of all the groups and who currently communicates with whom etc.
That way it would also be easy to add functionality on top, like group buying of tickets to shows for a lower price, or setting up events where all involved are to meet at a certain place at a certain time.
Actually my old Jiminy! SMS is intentionally a group messaging app, that uses SMS for sending messages. Modern group messaging apps don’t do that, but instead rely on wireless data. That way the performance will be much better, more complex data can be transferred, and it’s easier integrated with other services like Facebook, Twitter etc.