We present vapor pressure and high-resolution heat-capacity measurements of multilayer krypton films adsorbed on graphite. We have found a complex phase diagram including reentrant layering transitions for coverages higher than three layers. The third layering transition does not end in a condensation critical point as was previously expected. The second-layer melting transition is preceded by what may be a commensurate-incommensurate transition between the first and second layers.