As you level and undertake the SMN Job quests, you will automatically unlock the other two egis (Titan and Garuda). Incidentally they replace Topaz and Emerald Carbuncle respectively, thus they use the same ability icons on your hotbar (Summon I and II).

Additionally you can only unlock Titan and Garuda Egis (and thus do the later SMN Job quests) once you've defeated those Primals during the main storyline, so if you've fallen behind in your main story quests it would pay to definitely make your way through them first before doing the SMN Job quests.