DISCOVERING PLANETS AROUND NEARBY BRIGHT STARS HAS BEEN A PRIMARY GOAL OF THE K2 MISSION SINCE THE BEGINNING. AFTER NEARLY 20 CAMPAIGNS K2 HAS OBSERVED AND DISCOVERED SYSTEMS WITH A WIDE VARIETY OF PLANETS WELL-SUITED FOR FOLLOW-UP OBSERVATIONS. OBSERVATIONS OF THESE SYSTEMS WITH PRECISE RADIAL VELOCITIES OR TRANSMISSION SPECTROSCOPY COULD ADDRESS NUMEROUS QUESTIONS ABOUT THE EXOPLANET COMPOSITION ATMOSPHERES AND FORMATION HISTORIES. WE PROPOSE SHORT-CADENCE OBSERVATIONS AND ANALYSIS OF THREE PARTICULARLY WELL-SUITED PLANETARY SYSTEMS FOR FOLLOW-UP OBSERVATIONS: HIP 41378 GJ 9827 AND TRAPPIST-1. THESE SYSTEMS ARE ALL AMONG THE BEST KNOWN FOR TRANSIT TRANSMISSION SPECTROSCOPY AND EITHER HAVE BEEN OR ARE SCHEDULED TO BE OBSERVED WITH HST. THESE PLANETS REQUIRE FURTHER K2 OBSERVATIONS TO REACH THEIR FULL POTENTIAL AS BENCHMARK SYSTEMS FOR DETAILED FOLLOW-UP. THREE OF THE FIVE PLANETS AROUND HIP 41378 DO NOT HAVE PRECISELY MEASURED ORBITAL PERIODS (BECAUSE THEY ONLY WERE OBSERVED TO TRANSIT ONCE) AND CURRENTLY CANNOT BE FOLLOWED UP IN TRANSIT. PARAMETERS FOR THE SYSTEMS AROUND GJ 9827 AND TRAPPIST-1 CAN BE IMPROVED WITH CYCLE 6 K2 OBSERVATIONS TO MAKE FUTURE OBSERVATIONS MORE EFFICIENT AND IMPROVE THE INTERPRETATION OF FUTURE OBSERVATIONS. WE WILL ANALYZE K2 LIGHT CURVES PERFORM TRANSIT ASTEROSEISMIC AND DYNAMICAL MODELING TO EXTRACT BOTH PRECISE PLANETARY AND STELLAR PARAMETERS. OUR AIM IS TO SIGNIFICANTLY IMPROVE OUR UNDERSTANDING OF HIP 41378 BY DETECTING AT LEAST ONE (AND POSSIBLY ALL) OF THE THREE SINGLY-TRANSITING PLANETS IN TRANSIT DURING C18 OBSERVATIONS. WE WILL ALSO IMPROVE THE PRECISION OF PARAMETERS IN THE GJ 9827 AND TRAPPIST-1 SYSTEMS. WE WILL SEARCH FOR ADDITIONAL TRANSITING PLANETS AND PLACE CONSTRAINTS ON NON-TRANSITING PLANETS IN OUR ANALYSIS. OUR TEAM IS HIGHLY EXPERIENCED WITH K2 DATA AND THE VARIOUS TYPES OF ANALYSIS WE PROPOSE. WE WILL DELIVER LIGHT CURVE PRODUCTS FOR THESE THREE SYSTEMS TO THE MAST. THE RESULTS OF OUR PROGRAM WILL BE A WELL-CHARACTERIZED SAMPLE OF PLANETS AMENABLE TO DETAILED FUTURE OBSERVATIONS LIKE TRANSIT TRANSMISSION STUDIES WITH JWST. THESE PLANETS WILL LIKELY REMAIN UNIQUE EVEN DURING THE TESS ERA AS WELL-STUDIED BENCHMARK SYSTEMS DISCOVERED BY K2.