The photometric observations from the recent decade revolutionized our view on classical pulsators. Low-amplitude signals have been detected photometrically in addition to the dominant high-amplitude radial mode pulsations in many RR Lyrae stars and classical Cepheids. First overtone pulsators with an additional low-amplitude signal at a period ratio of around 0.61 with the main mode, the so-called 0.61 stars, form the most populous group among these stars. The nature of this signal has been attributed to non-radial pulsations. Another mysterious group are stars, where the additional signal forms a period ratio of around 0.68. These are the 0.68 stars. The origin of the signal remains unknown. Here, we search for similar phenomena in spectroscopic observations of first-overtone classical Cepheids collected as part of the VELOCE project. We performed frequency analysis of several parameters derived from cross-correlation functions (CCFs), including radial velocity (RV), full width at half maximum (FWHM), bisector inverse span (BIS), and CCF depth (contrast). Using standard prewhitening, we searched for additional low-amplitude signals. We identify the location of these stars in various sequences of the Petersen diagram. We detect additional signals in four first-overtone classical Cepheids: BG Cru, QZ Nor, V0391 Nor, and V0411 Lac. We classified BG Cru, QZ Nor, and V0391 Nor as 0.61 stars based on period ratios. V0411 Lac, however, exhibits a ratio of 0.68 between the two modes, and the additional signal has a longer period. This kind of multiperiodicity remains unexplained. VELOCE CCFs yield the first spectroscopic detections of non-radial pulsation modes in classical Cepheids. This opens an asteroseismic window for pursuing a more detailed understanding of these important stars. While the 0.61 signal of BG Cru, QZ Nor, V0391 Nor is understood to originate due to non-radial modes of moderate degrees, the 0.68 signal of V0411 Lac still lacks a physical explanation.