A novel family of $Ku$-band highly selective multi-band bandpass filters (BPFs) realized using groove-gap-waveguide (GGW) technology is presented. The conceived multi-band BPF structures are derived from a quasi-elliptic-type single-band prototype by applying a split-type single-to-multi-band frequency transformation. The baseline single-band prototype incorporates extracted GGW-rectangular-cavity sections at both the input and output accesses, which are preserved in the multi-band extension as multi-cavity tails. These extracted cavities enable the generation of multiple stopband transmission zeros (TZs) to obtain steep-attenuation characteristics in fully inductive-coupling filter structures without the need for cross-coupling mechanisms. Theoretical design examples of fourth-order dual-band and sixth-order triple-band filtering responses are developed using the coupling-routing-diagram formalism. These examples demonstrate the versatility of the proposed multi-band BPF approach in terms of bandwidths and center frequencies for passbands, spectral symmetry or asymmetry, and out-of-band TZ placement. For experimental-validation purposes, a proof-of-concept GGW dual-band BPF prototype exhibiting fourth-order passbands centered at 14 and 14.4 GHz and five stopband TZs is designed, manufactured, and measured. A compact two-layer vertically stacked GGW configuration is adopted for its physical implementation, confirming the practical feasibility of the proposed architecture. In addition, electromagnetic-simulation-based sensitivity analyses are performed to assess fabrication robustness, and a quantitative comparison with prior-art designs is provided to evaluate the RF-performance merits of the developed Ku band GGW dual-band BPF.