We investigate the formation of multiple spiral modes in Milky Way-like disk-halo systems without explicitly exciting perturbations. We explore how numerical resolution, the level of local disk stability, and the presence of a live halo influence both the initial appearance and the subsequent evolution of these modes. To characterize spiral structure, we compute Fourier amplitudes for modes
m=1-
6. In marginally unstable, lower-resolution disks (
N⋆=5×106,
NDM=1.14×107), faint features appear within the first
0.5 Gyr due to numerical noise, in contrast to high-resolution models where perturbations emerge later. Across all sufficiently resolved, live-halo models with
mDM/m⋆≤10, the spirals exhibit a cascading sequence in both mode number and radius: higher-
m modes form and decay first, followed by the delayed emergence of lower-
m modes, with an inward drift of the activity's epicenter. This behavior reflects a combination of local swing amplification, which explains the initial growth of short-wavelength modes, and interference between coexisting long-lived spiral modes, which accounts for the recurrent short-timescale amplitude modulations. In contrast, models with a fixed halo potential or coarse halo resolution (
NDM=1.14×106 and
mDM/m⋆=100) show strong early spirals but lack this coherent cascading behavior, owing to excessive shot noise and insufficient halo responsiveness. The
m=3 mode plays a transitional role, marking the onset of angular-momentum transport in the inner disk that precedes bar formation, a process absent in fixed-potential models. Our results show that a live halo with appropriate mass resolution provides the gravitational response needed to sustain and regenerate multi-mode spiral structure, even though the total angular-momentum exchange remains small.