No one on base
The plate ump (if he signals at all) should signal that he is staying at the plate.  On a base hit, he should move up the first base line watching for a swipe tag or a pulled foot, then rotate back to the plate.  The base ump has baserunner responsibilities on all three bags.
 
Runner on first base only
The plate ump signals that he is rotating to third  on a base hit and has the play there if R1 from first goes to third, and the play at the plate should R1 go home.  He has interference responsibilities at second on a double play as well as watching for a pulled foot or swipe tag on a first play at first base.  The base ump has all other plays on the infield, including the play on R1 at second on a force, and R2 at any bag.
 
Runner at second base only
The plate ump should signal that he is staying at the plate.  He still has swipe tag and pulled foot responsibilities at first, but doesn’t go too far up the line as he has the play at the plate if R1 from second attempts to score.  The base ump has all plays on the bags including R1 at third and the batter runner anywhere.
 
Runner at third only
The plate ump should signal that he is staying at the plate.  On a base hit, he has swipe tag and pulled foot responsibilities at first, but does so from 1st base line extended so that he’s in position should R1 from third attempt to score.  The base ump has all plays on the bags, including R1 diving back to third and the batter runner anywhere.
 
Runners at first and second
This is an infield fly situation with less than two outs.  The plate ump should signal that and indicate that he’s going to third IF R1 from second attempts to move up after tagging on a caught fly ball to the outfield.  Other than that he stays at the plate.  The base ump has all plays on the bases on R1 from first and on the batter runner.
 
Runners at first and third
This is a timing play situation with two outs and the plate ump should signal as such, as well as indicating that he’s moving to third should R2 attempt to move there on a base hit.  In doing so, he will watch R1 from third touch the plate watching over his shoulder as he moves to third.  If the first play is on the infield at 1st base, the plate ump moves slightly up the 1st base line to watch for swipe tags and pulled feet before proceeding to 3rd.  The plate ump also has interference responsibilities at second on the force.  The base ump has the play on R2 from first at second as well as the play on the batter runner on any bag.
 
Runners at second and third
This is a timing play situation with two outs and the plate ump should signal as such, indicating that he is staying home is all situations.  He still has swipe tag and pulled foot responsibilities at first base, but will do so from first base extended as he is also responsible for all pays at the plate.  The base ump has all plays on all runners on the bags.
 
Bases loaded
This is an infield fly situation with less than two outs and the plate ump should signal as such, also indicating that he is staying at home.  All plays on the bags belong to the base ump and the plate ump has all plays at second.  The plate ump has interference responsibilities at second on the force, and will watch for swipe tags and pulled feet from 1st base extended.
 
In every situation where possible without compromising his responsibilities at the plate, the plate ump will rotate either to 1st or 3rd to assist in a rundown.