EX

Carbuncle: all party members receive 10% less damage for 30 seconds from all sources. (it would normally be reflect but that isn't much of a mechanic in ff14)

Phoenix: Either revive all dead party members with 5% HP and a really long CD (healers better be quick or it wont stop a wipe) Or possibly puts a buff on the party and the next person to die in say 1 minute is auto raised with 70% HP and Mana.

Ifrit: Fire aspected damage and increase physical damage dealt to targets hit by 10% for 30 seconds.

Garuda: Wind aspected damage and increase magical damage dealt to targets hit by 10% for 30 seconds.

Bahamut: Large unaspected damage (Duh)

Etc Etc.

Then put each one of a timer and have like a minute shared recast between all summons and give individual summons their own recast timers that depend on how powerful they might be.