The simple answer is, "Agreement of the other members allows a new member to join."
The more complex question is, "What considerations do the members want to take in new members."
To my way of thinking, there's a range of issues:
1) Comparability. If you bring in a carrier you want to ensure that it offers a level of service which is comparable to the other members.
2) Network needs. A "global" network must cover the globe. The basics are mandatory: a strong US anchor, a top rank European carrier, and a top rank Asian carrier.
3) Avoidance of duplication. Alliance partners should not have to slug it out. (This is what fuels the rumours of TG being courted by SkyTeam).
4) Cost benefit. Every revenue passenger km you feed to an alliance partner should be balanced by revenue passenger km being fed from the carrier. In addition, every revenue passenger km you feed out of the network, is an opportunity lost.
5) Willingness and ability to cooperate. Airlines participate in other ways, such as joint purchasing.
6) Optimization. Too few carriers and you don't offer a network or range of service that is attractive enough. Too many carriers, and the demands on individual areas can prevent delivery of services.
Each of these issues is relative. Some might question the comparability of, say, BD and SQ, but, domestic British traffic has to go somewhere. Better in the club than out. Similarly, Africa is not well covered, other than through FRA. But would Ethiopian really be a welcome addition? (Actually as African carriers go, they're not bad, but that is, after all, a relative statement).
It seems clear that * considers its present size to be just about right, as they move from an expansion mode, to a cooperation mode. With 13 carriers (15, actually, if you include all three Austrian brands), there are only two additions I can see coming down the pipe: CP (if only as it gets merged into AC), and EK (there is a big hole in the network in the Gulf, and Emirates would be a huge coup). Beyond that, the world is pretty much covered.