Reentrant cavities are microwave resonant devices employed in a number of different areas of physics. They are appealing due to their simple frequency tuning mechanism, which offers large tuning ranges. Reentrant cavities are, in essence, 3D lumped LC circuits consisting of a conducting central post embedded in a resonant cavity. The lowest order reentrant mode (which transforms from the TM010 mode) has been extensively studied in past publications. In this work, we show the existence of higher order reentrant post modes (which transform from the TM01 n mode family). We characterize these new modes in terms of their frequency tuning, filling factors, and quality factors, as well as discuss some possible applications of these modes in fundamental physics tests.