Yes, by installing Trimble's Mapping and GIS License Manager software on a network server, you can manage multiple licenses for the GPS Analyst extension. Using the GPS Analyst License Administrator software, GPS Analyst extension users can choose either a Single Use or a Floating license. http://trl.trimble.com/docushare/dsweb/Get/Document-512365/GPSAnalyst_GSG_ENG.pdf
This isn't done from within ArcMap, you would use the Trimble GPS Analyst License Administrator software for this purpose. Please review Chapter 2 of the Getting Started Guide for Trimble GPS Analyst Extension, http://trl.trimble.com/docushare/dsweb/Get/Document-512365/GPSAnalyst_GSG_ENG.pdf. Starting at page 30 you will find information on installing the Mapping and GIS License Manager software. For more information search for the topic, GPS Analyst License Administrator, in the Trimble GPS Analyst Extension Help.