Germany waits for an opening in the Philippines

Were other empires tempted to take Spanish possessions in the same way as the United States?

Yes - Germany in particular hoped the Americans might leave the Philippines, creating an opportunity for Berlin to move in.

Germany was the clearest rival power tempted to exploit Spain's colonial weakness. During the interval between Dewey's victory and the arrival of American troops, German ships watched for signs that the United States might withdraw. Berlin's desire for a place in the sun made the Philippines attractive and created friction with the American squadron. The episode shows that defeating Spain did not end naval competition around the islands; it transferred the colonial question into a wider contest among rising powers.