For my case I'm wondering if I can cast Enlarge twice on an Adult Blue Dragon so I can enlarge it enough so it would get stuck in the cave that I'm fighting it in, causing it to be Restrained in it's own lair. Would this work? Thoughts?

enlarge/reduce requires concentration, so you may only have one instance of it active at once.

And generally, no, spell effects do not stack with themselves.

Under Combing Magical Effects in the DMG:

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect — such as the highest bonus — from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.

For example, if two clerics cast bless on the same target, that character gains the spell’s benefit only once; he or she doesn’t get to roll two bonus dice.

So enlarging an already enlarged creature doesn't do anything but reset the duration of the effect.

From the section on combining spells in the PHB: “The effects of the same spell cast multiple times don't combine, however.”

Even if you had multiple characters casting Enlarge on the target, the target will only be subject to the effect of one of them. 

I will note, the rules say the effects do not combine; they do not say one of the effects does not happen.  There could be a situation where you double cast enlarge to ensure that, if one of the players loses concentration, the spell effect might continue due to the other player retaining concentration.  I am guessing those situations are few and far between though - you would have to really want an effect to persist in order to burn two character’s concentrations on that effect.