I came across a scenario recent;y where my 4 PS 2 ships were firing at another PS 2 enemy. I had the initiative and destroyed it with my 3rd ships shooting including. But I still had my other ship to fire so could I still fire at it in the hope of getting a crit to stop it shooting back, eg Blinded Pilot etc.
Crits vs Hull
I think you forgot to ask a question.
If your question was: Can I keep shooting at a ship that already has damage cards in excess of it's hull value?
Then the answer is: Yes.
As Klutz mentions a ship can acquire more damage cards than it has hull value.
Now I'd normally say that putting cards on a ship that is going to be destroyed is a waste aside from a little more information to use for statistical calculations but you have a case where it may be very valuable to throw on more damage cards hoping to get that one face-up card that alters the soon to be deceased ship's activities.
I guess it could be pointed out that sometimes a person may even have to shoot at a ship that is going to be destroyed! Say you've got initiative and a bunch of ships shooting at the same PS as Biggs; every ship that can shoot at Biggs must shoot at Biggs even if he already drew his third damage card with the first attack.
The other thing to look at might be - can the 'destroyed' ship one-shot one of my ships in it's dying attack? Does it have the offensive firepower to do that? If not, why bother attacking it again? I probably wouldn't waste further shots on it unless it was still a major threat.
If the soon to be destroyed ship is the only legal target, go ahead and shoot regardless of other considerations.
If the soon to be destroyed ship is the only legal target, go ahead and shoot regardless of other considerations.
I suppose there's no such thing as overkill, is there?
When I was playing paintball, I always believed every paint job needs a second coat. 
If the soon to be destroyed ship is the only legal target, go ahead and shoot regardless of other considerations.
I suppose there's no such thing as overkill, is there?
There is no such thing as overkill. Only "reload" and "fire".