Typically the motion process provides the following filing scenario: first moving papers filed, then opposition by the other side, then a reply brief by you. If you made a mistake or other material error in the moving papers, you can file an amended brief with the changes- you want to do this before the opposition comes in. If you want to expand on the points raised in the original filing, you could also take the motion off calendar and set a date later in the year and then the timeline starts over again. If it is a minor issue, you can include it in your reply papers, although those are supposed to be limited to responding to the points raised in the opposition.
This is not intended as legal advice and should not be relied upon as search. Each case is different, and you should consult an attorney for specific analysis of your situation.
I understand your question to mean that the case has been taken up on appeal to the federal Circuit Court of Appeals and now the appellant wants to go back to district court, while the appeal is still pending, with a motion of some kind. Depending on the subject matter of the motion, this might be allowed but the appellant should understand the district court loses jurisdiction over most matters in the case while the appeal is pending. So you have not given enough information in your question for any counsel to be able to answer it.
Now, if the appellant is appealing to the U.S. District Court from the decision of an administrative agency or from a decision of the bankruptcy court, etc., then there is a much broader subject matter for motions. Still, counsel can't answer your question as to whether the motion the appellant wants to file is allowed without knowing much more about the facts and proceedings so far in the appeal.
Cal. Bar No. 104800
Wis. Bar No. 1020123