TRANSITING PLANETS FROM THE KEPLER K2 AND TESS MISSIONS PRESENT AN OPPORTUNITY TO MEASURE THE RADII OF VERY SMALL PLANETS APPROACHING THE SIZE OF THE EARTH (AND EVEN SMALLER). HOWEVER FOR THE MAJORITY OF THESE SYSTEMS WE CANNOT MEASURE THE MASSES OF THESE PLANETS FROM RADIAL VELOCITY: EITHER THE STARS ARE TOO FAINT AND/OR THE RADIAL VELOCITY AMPLITUDES TOO SMALL. SO THE QUESTION REMAINS: WHAT ARE SMALL PLANETS MADE OF? MOSTLY ROCK AND IRON? IF SO HOW MUCH OF EACH? OR A GASEOUS ENVELOPE AS WELL? HERE WE PROPOSE TO IMPROVE THE CONSTRAINTS UPON THE COMPOSITIONS OF TRANSITING EXOPLANETS WITH PHOTODYNAMICAL CHARACTERIZATION OF MULTI-PLANET SYSTEMS. WE WILL TAKE A TWO-PRONGED APPROACH TO THIS PROBLEM: A). BETTER CHARACTERIZING PLANET RADII IN MULTI-PLANET SYSTEMS TO REFINE THE RADIUS VALLEY MEASUREMENTS B). MEASURING PLANET MASSES FROM TRANSIT-TIMING IN A SUBSET OF THESE SYSTEMS. THE DISTRIBUTION OF PLANET SIZES AT SHORT ORBITAL PERIODS HAS A MINIMUM NEAR ~1.8 TIMES THE RADIUS OF EARTH REFERRED TO AS THE "RADIUS VALLEY" OR "FULTON GAP." THIS GAP HAS BEEN ATTRIBUTED TO MULTIPLE POSSIBLE ORIGINS WHILE EACH OF THESE MODELS MAKES PREDICTIONS FOR THE DEPENDENCE OF THE GAP ON THE PLANET ORBITAL AND STELLAR PROPERTIES. HOWEVER DISTINGUISHING BETWEEN THESE MODELS IS CURRENTLY LIMITED BY I). THE PRECISION OF THE MEASUREMENTS OF PLANETARY RADII AND II). THE SMALL SIZE OF THE SAMPLE OF PLANETS WITH HIGH-PRECISION MEASUREMENTS. WE PROPOSE TO DEVELOP A PATH TOWARDS REFINING PLANETARY RADIUS MEASUREMENTS FOR A SIGNIFICANT NUMBER OF TRANSITING MULTI-PLANET SYSTEMS IN THE KEPLER K2 AND TESS DATASETS. THERE ARE TWO BARRIERS TO MEASURING PLANETARY RADII WITH HIGH PRECISION FROM TRANSITING PLANET DATA: UNCERTAINTIES ON THE PLANET-STAR RADIUS-RATIOS THANKS TO DEGENERACY WITH IMPACT PARAMETER AND LIMB-DARKENING AND UNCERTAINTIES ON THE STELLAR RADIUS MEASUREMENTS. MULTI-PLANET SYSTEMS OFFER THE PROSPECTS FOR ADDRESSING THESE LIMITATIONS WITH BETTER CHARACTERIZATION OF BOTH THE PLANETS AND THE STAR. OUR TOOL WILL BE A PHOTODYNAMICAL MODEL WHICH COMBINE PHOTOMETRY AND DYNAMICS TO MODEL THE ENTIRE TRANSIT LIGHT CURVE SIMULTANEOUSLY. A JOINT ANALYSIS OF THE PLANETS WILL SOLVE BOTH PROBLEMS: IT WILL BREAK THE DEGENERACY BETWEEN PLANET RADIUS AND IMPACT PARAMETER AND IT WILL PROVIDE A MORE PRECISE ESTIMATE OF THE STELLAR DENSITY. TOGETHER WITH LUMINOSITY/TEMPERATURE ESTIMATES FROM GAIA THIS WILL PROVIDE PRECISE CHARACTERIZATION OF THE PLANETARY RADII. WE WILL LEVERAGE TOOLS WE HAVE BEEN DEVELOPING OVER THE LAST FEW YEARS TO CREATE A FULLY DIFFERENTIABLE PHOTODYNAMIC MODEL ACCOUNTING FOR CORRELATED NOISE. WE WILL THEN USE A HAMILTONIAN MONTE CARLO APPROACH TO INCREASE THE EFFICIENCY OF SAMPLING THESE HIGH DIMENSIONAL SYSTEMS. WE HAVE DEMONSTRATED THIS CAPABILITY WITH THE TRAPPIST-1 SYSTEM IN WHICH CASE THE STELLAR DENSITY IS DETERMINED WITH A PRECISION OF ~2% WHILE THE PLANETARY RADII ARE DETERMINED WITH A PRECISION OF 1-2%. WE PLAN TO APPLY A SIMILAR METHODOLOGY TO THE KEPLER K2 AND TESS MULTI-PLANET SYSTEMS FOR WHICH THERE ARE 10^3 PLANETS WITH PERIODS &LT; 100 DAYS WHICH STRADDLE THE RADIUS VALLEY. IN A SMALL NUMBER OF CASES WE CAN MEASURE MASSES OF THE TRANSITING EXOPLANETS FROM PHOTODYNAMICS BASED UPON TRANSIT-TIMING VARIATIONS (TTVS). WE WILL HELP TO REFINE THE MASS-RADIUS RELATION OF SMALL EXOPLANETS WITH OUR ANALYSIS CONSTRAINING THEIR BULK DENSITIES WHICH PROVIDES CONSTRAINTS ON THE COMPOSITIONS WHICH COMPLEMENT TO THE RADIUS VALLEY MEASUREMENTS. IN SUM WE WILL DEVELOP A SAMPLE OF ORDER 10^3 PLANETS WITH PRECISELY MEASURED RADII TO CONSTRAIN THE RADIUS VALLEY TO HIGHER PRECISION THAN IS CURRENTLY POSSIBLE. FOR A SUB-SAMPLE OF ORDER 10^2 PLANETS WE WILL MEASURE MASSES WITH TTVS YIELDING CONSTRAINTS ON THE PLANETS' DENSITIES AND COMPOSITIONS. TOGETHER THESE RESULTS WILL BE THE ABILITY TO BETTER TEST MODELS FOR THE ORIGIN OF THE VALLEY AND THE COMPOSITIONS OF SMALL EXOPLANETS.