Yes, you can support a foreign unit to attack your own unit. However, if your unit would be dislodged by the attack, then your support is cancelled; the attack will still succeed if there are enough other supports.
There actually *is* a tactical reason that you may wish to do this, although I've only very rarely seen it come up in an actual game. In one particularly fun example, I was a Germany with F NTH, F HEL, A Hol, A Kie, England ready to retake NTH from Edi/Yor/Lon because French ENG was otherwise occupied convoying to Wales and Russia in Nwy/SKA/Den with three fleets that had been keeping me there but now seemed to want NTH for himself. So I ordered Hol - NTH - Den with Kie support. If I did nothing else, by the way, you get a fun problem trying to resolve this orderset assuming a power-3 English Yor - NTH and power-3 Russian SKA - NTH, because dislodging Den would cancel its support, but an attack via disrupted convoy would not. However, I didn't want that particular outcome anyway, and found something better by adding HEL S SKA - NTH...
Another way of using this is, given a sufficiently crowded theater, to even order one support for each side, trying to guarantee a standoff. :)