Debris disks around main sequence stars are remnants of successful planet formation. Studies of debris disks have revealed an immense diversity in their morphologies. Recently, sub-millimeter ALMA observations of debris disks around 4 stars (HD 107146, HD 92945, HD 15115, and HD 206893) spatially resolve multiple debris rings separated by a cleared gap. We assumed all gaps were formed through secondary dynamical planet-disk interaction and investigated the applicability of gap carving mechanisms proposed in the literature to recreate the observed structure using an N-body code, REBOUND. For each N-body simulation, we produced a synthetic ALMA image with the same viewing geometry and resolution as the observations, and then compared the radial intensity profile of our models with the data. We attempted to recreate each observed gap using (1) a planet in situ clearing particles in its chaotic zone, (2) a set of inner planets in mean motion resonance (MMR) clearing gaps in a resonance chain, and (3) secular interactions between a low-mass inner planet and a disk. We were able to reproduce all four disks with the first mechanism. Although we were able to open gaps at the right location with the second mechanism, a planet sufficiently massive and at the right location to carve a resonance gap pushed out the inner edge of the disk to a radius inconsistent with all of the observed disks. The third mechanism was capable of producing a morphology similar to the disks around HD 107146 and HD 92945, but could not produce a gap with sufficiently steep edges to match observations of the disk around HD 15115, and was not possible in combination with HD 206893’s directly imaged brown dwarf companion. When considered as an ensemble, our results show that while inner planets in MMRs are probably not a common mechanism for producing observed debris disk gaps, secular interactions with low-mass inner planets should routinely be considered as an alternative to the standard in-situ assumption.