Jamie Brace's answer is already spot on, any hit is automatically a critical hit, and multiple instances of criticals don't stack.
But here's where it would actually matter:
Say you're up against a surprised enemy with 26 AC, and only have an attack bonus of +5. Due to the wording on Assassinate, you'd only score a critical hit on this creature only if you hit. With only a +5 bonus, you'd need a 21 on a d20 roll to hit- impossible... unless it's a critical hit.
One of the perks of rolling a 20 is (found in PHB 194):
Rolling 1 or 20
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC.
So, given the above situation, you'd only be able to assassinate on a roll of 20.
"ok, daze, that's a corner case, but it isn't really that cool."
Yes, by RAW it's pretty lame but you're the GM and it's your job to make things interesting.
Your specific situation has never come up in my games yet, but I do have an Assassin rogue, so it very well might. However, I do have this little houserule that covers something similar:
Whenever someone rolls two d20s, either Advantage or Disadvantage, and rolls two 20s, I add a little extra minor mechanical effect, depending on the situation, to make the roll more awesome.
These benefits aren't written down anywhere (I don't have a table to look up when this happens), I just decide what would be a cool effect. Here are some examples of the effects I've doled out, so you can get an idea of how minor it is and come up with some of your own:
- Shoving a Grell that was grappling an ally 10 feet (this was a critical despite disadvantage).
- Ending the grapple of a Rug of Smothering that was choking an ally.
- Dropping a Thug, just 5 HP short of dead, unconscious.
In your case, it would depend on the situation, if it were a humanoid with relatively low HP but not quite like the Thug above, I'd make him stunned until the end of his next turn. If it were a big nasty, I'd make it prone. Work it out and get creative!