Well, Spain, Belgium, and the Netherlands signed the Boxer Protocol without being part of the Eight-Nation Alliance so they seem like obvious and easy candidates for inclusion. Really, each of them could very feasibly send a contingent, even a mostly nominal one, to participate in the Alliance. That gets us to 11 nations (and every country that had a legation in Beijing IOTL)
Portugal is the next most obvious participant. They have important interests in China so the need is addressed. IOTL it seems they focused their effort on protecting Macau and expanding their influence in the adjoining region instead of sending forces north to Tianjin with the multinational force. But they did get reinforcements shipped in from Portugal itself, so clearly the ability to deploy additional forces to China existed. Best POD would seem to be Portugal opening a Beijing legation and thereby having a reason to join the Alliance.
Next best option is Sweden-Norway. IOTL they were the fourth power to sign a treaty with China post-opium war, so clearly the interest in Chinese concessions existed. But I don’t think Sweden-Norway ever acquired actual territorial concessions. So I think the best way to get Sweden-Norway involved is to have them acquire a concession and/or a Beijing legation to motivate participation.
So, that comes to a grand total of 13 nations.
Really the only other possibilities are the South American nations. And I simply don’t see any of them having the interest to participate.