FOLLOWING A SERIES OF REMARKABLE RECENT DISCOVERIES WE NOW KNOW THAT SOME OF THE MOST LUMINOUS MEMBERS OF THE ULTRALUMINOUS XRAY SOURCE (ULX) POPULATION ARE ACTUALLY POWERED BY HIGHLY SUPER-EDDINGTON NEUTRON STAR ACCRETORS. THREE SUCH SYSTEMS ARE NOW KNOWN: M82 X-2 NGC 7793 P13 AND NGC 5907 ULX1. HERE WE PROPOSE ~WEEKLY SWIFT MONITORING OF THE LATTER TWO OF THESE SYSTEMS WHICH ARE SUFFICIENTLY ISOLATED FOR SWIFT TO PROVIDE ROBUST FLUXES ACROSS THE FULL VISIBILITY WINDOW AVAILABLE FOR EACH SOURCE IN THE UPCOMING CYCLE. THESE OBSERVATIONS WILL HELP TO REVEAL THE NATURE AND PHYSICAL PROPERTIES OF THE MOST EXTREME ACCRETORS KNOWN.