A frequency-degenerate cavity (FDC) is the resonator that the ratio of transverse and longitudinal mode frequency spacings is a simple rational number. When an optical resonator is close to the FDC, transverse-mode-locking (TML) takes place with drastic changes of laser mode. We report for the first time, to the best of our knowledge, the multi-frequency emission and spectral modulation effects coupled with TML in FDC. The Yb:CaGdAlO₄ (Yb:CALGO) crystal with large gain bandwidth was used as a gain medium in an off-axis-pumped hemispherical FDC for realizing broadband emission. Interestingly, the spectrum can transform from a single smooth packet shape to a multi-peak structure; meanwhile, the transverse pattern accordingly transforms into some exotic wave-packet profiles through controlling off-axis displacement in a special degenerate state.