Hi - my name is XXXXX XXXXX I'm a Family Law litigation attorney. Thanks for your question.
Yes, it is possible for your ex to file a motion to modify custody. However, in order to authorize a change of custody, the party who brings the action must show that (a) there has been a material change of condition (b) substantially affecting the interest and welfare of the child, and (c) the evidence offered to prove such condition must be fresh, having occurred since the most recent custody award. A slight change in condition will not authorize a change of custody, and each case is fact specific.
Thus, in this case, your ex would have to be able to prove that there has been some change to justify a modification of custody. This would be something like a remarriage, child abuse, substance abuse, the parent moves, etc. If there's been no such change, then there is very little likelihood that a modification would be allowed.
I hope this answers your questions, but if you have others, please REPLY and I'll be glad to respond.