I stumbled upon this sentence on the first episode of Midnight Diner:
It gets translated to something like:
The president over there asked me to dance a little more.
If I were to write the “asked me to dance” part myself I would go for something like:
I have done some google searches but I had no luck so far finding a ないかって grammar pattern. Is the かって supposed to be actually 勝って. That would still make no sense in my somehow intermediate Nihongo mind but it would get kind of closer.