The PHB states:
Using at least one free hand, you try to seize the target by making a grapple check
But if the grappler has another free hand, can he grapple the same target again, with the other hand?
More importantly, if this is all possible, and the character successfully grapples the target with multiple limbs, does that mean the target will have to use an action, and succeed, for each grapple, to break free?
The idea is that a strong grappler can maximize the probability of keeping a target grappled by using more limbs. And a grappler with many limbs, can increase those odds even more.