Can a party file a response to a cross-motion in federal court?

I agree with my colleagues. I also offer that it is best if parties can coordinate briefing schedules to try to avoid extra paperwork. This is one reason parties are required to "meet and confer" before filing most motions in federal court. A common practice involving cross motions is: (1) opening motion; (2) combined cross motion/response to first motion; (3) combined reply in support of first motion/response to cross motion, and; (4) reply in support of cross motion. Good luck.

Generally speaking (without knowing the specific nature of the motion and cross-motion), yes, the plaintiff can file an opposition to the defendant's cross-motion. If you are in the U.S. District Court for the Central District of California, make sure each side confers prior to filing any motion. (See Local Rules 7-3 and 7-4, and also Local Rules 7-9 and 7-10).

While I cannot give you legal advice in this forum, here is some general information that may be useful. As a general matter, if a motion is filed (regardless of how it is titled) you can always file an opposition. The procedure for doing so varies within each Federal District Court. Therefore, check the local rules. In the Central District of California, check Local Rules 6 and 7 for general non-discovery related motions.