I flew IAH-LAX-HNL-GUM-ROR-GUM-SPN-GUM-PNI-HNL-IAH a few years ago. The ticket allowed 1 stopover (GUM). But I found there was an evening GUM-PNI flight that allowed a 13-hr layover before continuing on the island hopper the next day. As a bonus I was upgraded PNI-HNL (*G).
I was able to get out in TKK, KSA and MAJ. They make everyone get off in MAJ anyway for security check.