Twenty years ago, GRB 980425/SN 1998bw revealed that long Gamma-Ray Bursts (GRBs) are physically associated with broad-lined type Ic supernovae. Since then more than 1000 long GRBs have been localized to high angular precision, but only in ∼ 50 cases the underlying supernova (SN) component was identified. Using the multi-channel imager GROND (Gamma-Ray Burst Optical Near-Infrared Detector) at ESO/La Silla, during the last ten years we have devoted a substantial amount of observing time to reveal and to study SN components in long-GRB afterglows.Here we report on four more GRB-SNe (associated with GRBs 071112C, 111228A, 120714B, and 130831A) which were discovered and/or followed-up with GROND and whose redshifts lie between z = 0.4 and 0.8. We study their afterglow light curves, follow the associated SN bumps over several weeks, and characterize their host galaxies. Using SN 1998bw as a template, the derived SN explosion parameters are fully consistent with the corresponding properties of the so-far known GRB-SN ensemble, with no evidence for an evolution of their properties as a function of redshift. In two cases (GRB 120714B/SN 2012eb at z = 0.398 and GRB 130831A/SN 2013fu at z = 0.479) additional Very Large Telescope (VLT) spectroscopy of the associated SNe revealed a photospheric expansion velocity at maximum light of about 40 000 and 20 000 km s −1 , respectively. For GRB 120714B, which was an intermediate-luminosity burst, we find additional evidence for a blackbody component in the light of the optical transient at early times, similar to what has been detected in some GRB-SNe at lower redshifts.