Not really a downside to asking, but you need to be sure that they are very, very keen to have you! And I wouldn't ask for a sign on bonus outright (just seems a bit rude) - just jostle for an increase in salary and they'll ususally say either (1) No chance (2) Increase the salary or (3) Keep the salary the same but offer a sign on. It all depends on how essential you are to their business plans going forward...