It went past me on the radio as I was going to sleep, so I didn’t get the details of either form or context, but the crux of the matter was the possibility of either can or can’t in
I’ll see if we can/can’t [do something or other]
Huge numbers of both on the net. Compare these two:
I’ll see if we can’t do something for you in the next version. (link)
But I’ll see if we can do something for you so you can try it out. (link)
At first glance, it looks like this is a case of simple negation indifference (as Chris Potts labeled it in 2004): adding or removing a negation without change of meaning.
There are (vaguely) parallel cases that Potts inventories (and that I’ll look at in a moment), but this one has its own assemblage of features, three different factors. And, I’ll argue, the variants are semantically close but nevertheless distinct.