A new class of reconfigurable frequency selective structures (FSSs) is proposed to operate across a wide band of frequencies. Specifically, thick FSSs are proposed with several desirable properties, including sharp roll-offs for narrow rejections. Similar to multi-stage filters, this higher-order selectivity enables frequency and bandwidth control. However, practical application requires the ability to tune these structures. The proposed design introduces a novel geometry to achieve reconfigurable frequency control for multi-band FSSs. The technique focuses on a bent dipole element with many different arm lengths for even greater selectivity and narrower rejection bandwidth. The proposed multi-arm design allows for tuning and control of the band rejection width. The subject FSS structures are extended to band-pass designs, and various element geometries are explored in terms of frequency and bandwidth control. A primary design focus is performance stability with respect to incidence angle and polarization.