A few teams have beat all 3.
Atlanta
Orlando
Indiana
Houston
OKC which makes sense
Philly has beat Cleveland and Boston. 0-3 against NYK, but they play them once more.
As far as adding guys this summer. They have no cap space to do it. They will basically have the MLE ($14 million) and most of that will be spent on keeping Beasley. No 1st round draft pick, either.
Technically, they can get to $20 million in space. But if Cade makes all NBA, and he should, they owe him more money on his extension. So instead of it being a $38 million cap hit next year, it will be around $46 million. That eats up the extra $6 million. So figure on $14 million without any trades.