If you're looking to switch things up from using the phrase "cross swords with", here are some potential synonyms to consider: clash with, come to blows with, engage in battle with, lock horns with, spar with, wrangle with, combat with, contend with, skirmish with, tangle with, have a feud with, oppose vigorously, or butt heads with. While each of these phrases carry a slightly different connotation, they all imply a level of conflict or opposition between two parties. Consider which specific shade of meaning you're trying to convey before choosing the most appropriate synonym for your context.