Context. In early-type Be stars, groups of nonradial pulsation (NRP) modes with numerically related frequencies may be instrumental for the release of excess angular momentum through mass-ejection events. Difference and sum/harmonic frequencies often form additional groups. Aims. The purpose of this study is to find out whether a similar frequency pattern occurs in the cooler third-magnitude B7-8 IIIe shell star ν Pup. Methods. Time-series analyses were performed of space photometry with BRITE-Constellation (2015, 2016/17, and 2017/18), SMEI (2003–2011), and HIPPARCOS (1989–1993). Two IUE SWP and 27 optical echelle spectra spanning 20 years were retrieved from various archives. Results. The optical spectra exhibit no anomalies or well-defined variabilities. A magnetic field was not detected. All three photometry satellites recorded variability near 0.656 c/d which is resolved into three features separated by ∼0.0021 c/d. Their first harmonics and two combination frequencies form a second group, whose features are similarly spaced by 0.0021 c/d. The frequency spacing is very nearly but not exactly equidistant. Variability near 0.0021 c/d was not detected. The long-term frequency stability could be used to derive meaningful constraints on the properties of a putative companion star. The IUE spectra do not reveal the presence of a hot subluminous secondary. Conclusions. ν Pup is another Be star exhibiting an NRP variability pattern with long-term constancy and underlining the importance of combination frequencies and frequency groups. This star is a good target for efforts to identify an effectively single Be star.