Magnetohydrodynamic waves redistribute energy in magnetic structures of the lower solar atmosphere, yet constraints on how wave power and dominant frequencies are organized above sunspots remain limited, because most studies use only a few well-separated diagnostics. Here, we present multiline wave signatures in a sunspot from near-ultraviolet (near-UV) spectroscopy with the SUNRISE-III UV Spectropolarimeter and Imager (SUSI). We analyse a 2 hr time series of repeated raster scans of a sunspot near disc center in the 327─329 nm spectral window (>100 lines). From these, we select 44 lines that radiative-transfer calculations suggest sample effective formation heights within the umbral core, from the deep photosphere toward the low chromosphere. For each line, we extract line-core intensity and line-of-sight velocity time series using a dedicated multiline fitting routine and compute Morlet wavelet power spectra. The refined global wavelet spectra show that most lines (in both intensity and velocity) are genuinely multifrequency, with a dominant peak and substantial statistically significant power up to 12 mHz. Unsupervised clustering of the normalized spectra groups lines into families with similar spectral shapes and reveals a progression of dominant frequencies from ∼2 to ∼10 mHz across the ensemble, for both intensity and velocity (not necessarily in the same lines). This behavior is not reproduced by a simple formation-height ranking, suggesting that uncertainties in the formation-height estimates and line-dependent diagnostic response together shape the ordering. These SUNRISE-III/SUSI observations open a new regime for near-UV multiline wave studies and provide the first systematic characterization of frequency-structured sunspot wave behaviour in this spectral region.