Although the FAA (9 USC 3) appears to require a district court to stay pending court proceedings when it compels arbitration, binding 9th Circuit precedent holds that, instead, a district court may dismiss the litigation if it compels arbitration of all claims raised in the case.  See Johnmohammadi v. Bloomingdale’s,Inc., 755 F.3d 1072, 1074 (9th Cir. 2014).  The two-judge concurrence urges rehearing en banc or the grant of certiorari to clarify this point.