WHAT ARE THE PROPERTIES OF ACCRETION FLOWS IN VICINITY OF COALESCING MASSIVE BLACK HOLE BINARIES (MBHBS)? THE ANSWER TO THIS QUESTION HAS DIRECT IMPLICATIONS FOR THE FEASIBILITY OF COINCIDENT DETECTIONS OF ELECTROMAGNETIC (EM) AND GRAVITATIONAL WAVE (GW) SIGNALS FROM COALESCENCES. SUCH DETECTIONS ARE CONSIDERED TO BE THE NEXT OBSERVATIONAL GRAND CHALLENGE THAT WILL PROVIDE A MORE COMPLETE UNDERSTANDING OF EVOLUTION AND GROWTH OF THESE MASSIVE OBJECTS. IN ANTICIPATION OF FUTURE DETECTIONS BY THE LASER INTERFEROMETER SPACE ANTENNA (LISA) WE PROPOSE TO INVESTIGATE THE COINCIDENT EM AND GW SIGNATURES OF MBHBS IMMERSED IN ACCRETION FLOWS. THE PROPOSED PROGRAM OF RESEARCH CENTERS ON A SUITE OF HIGH-RESOLUTION SIMULATIONS WITH THE RADIATION-MAGNETOHYDRODYNAMIC CODE ATHENA++ WHICH WILL FOLLOW BINARIES AS THEY EVOLVE THROUGH THE LISA FREQUENCY BAND. THIS STUDY WILL SET THE STAGE FOR THE FIRST SIMULATIONS OF ACCRETING MBHBS WITH RADIATIVE TRANSFER AND WILL USE THEM TO PREDICT THE RESULTING EM SPECTRA LIGHT CURVES AND GRAVITATIONAL WAVEFORMS.