I reckon it'd take more than
a supernova to saturate your neutrino detector. Especially if you're using the current ones based on underground tanks of chlorinated water
( sandettie light vessel automatic New Twitter - @bollocksreally, Wed 22 Jun 2011, 16:37, 2 replies, latest was 14 years ago)

If it was the sun, then I'd say you're fucked.

(Shippy likes linebreaks and doesn't care what you think, Wed 22 Jun 2011, 20:20, Reply)

Oh no, my neutrino detector is saturated
* vapourises.
( sandettie light vessel automatic New Twitter - @bollocksreally, Wed 22 Jun 2011, 22:40, Reply)

fwiw
I think being in an earth orbit around sn1987a would have saturated them. Mind you, I did work this out in my head whilst in a bus on the way home from uni in (erm) 1987. Might not be completely reliable.
(haberman is singing in the changes, Mon 27 Jun 2011, 17:32, Reply)