It should mean as follows:
That you can have summon one after another. So if the lifespan of your familiar has finished, you can recast spell again.
Kooldown- Aid does not give double effect, means if the spell is still active, will not be activated again (summon spell is active for 15 minutes or just for the life-spine of the summon). Same goes for intense recovery- you will not be healed double by resetting cool-down of the spell.
I believe in that case you would just overide the previous spell. Means,
14:00 - You activated spell - Intense Recovery or Familiar
14:07- You used Kool-down kit
14:07 - you recast the spell- the previous is being cancelled, and new span of the spell is activated
Nice trying there though. xD