20 CFR §1002.120

No. The employee has reemployment rights with the pre-service employer provided that he or she makes a timely reemployment application to that employer. The employee may seek or obtain employment with an employer other than the pre-service employer during the period of time within which a reemployment application must be made, without giving up reemployment rights with the pre-service employer. However, such alternative employment during the application period should not be of a type that would constitute cause for the employer to discipline or terminate the employee following reemployment. For instance, if the employer forbids employees from working concurrently for a direct competitor during employment, violation of such a policy may constitute cause for discipline or even termination.