On our cluster, tribes are allowed to a single alliance with up to 4 players max.
You can only be in ONE alliance.
Our system governs by players, not tribes.
Be sure you only have ONE alliance created in your alliance manager. Creating additional alliances can prevent you from inviting others into your alliance.
If you are being invited into an alliance, be sure you have no alliances already existing in your alliance manager. This can prevent you from being invited into an alliance.