Context. We present the current status of and new results from our search for exoplanets in a sample of solar-mass evolved stars observed with the HARPS-N and the 3.6 m Telescopio Nazionale Galileo (TNG), and the High-Resolution Spectrograph (HRS) and the 9.2 m Hobby-Eberly Telescope (HET). Aims. The aim of this project is to detect and characterize planetary-mass companions to solar-mass stars in a sample of 122 targets at various stages of evolution from the main sequence to the red giant branch, mostly subgiants and giants, selected from the Pennsylvania-Toruń Planet Search sample, and to use this sample to study relations between stellar properties, such as metallicity, luminosity, and the planet occurrence rate. Methods. This work is based on precise radial velocity (RV) measurements. We have observed the program stars for up to 14 yr with the HET/HRS and the TNG/HARPS-N. Results. We present the analysis of RV measurements with the HET/HRS and the TNG/HARPS-N of four solar-mass stars, HD 4760, HD 96992, BD+02 3313, and TYC 0434-04538-1. We found that HD 4760 hosts a companion with a minimum mass of 13.9 MJ (a = 1.14 au, e = 0.23); HD 96992 is a host to a m sin i = 1.14 MJ companion on an a = 1.24 au and e = 0.41 orbit, and TYC 0434-04538-1 hosts an m sin i = 6.1 MJ companion on an a = 0.66 au and e = 0.08 orbit. In the case of BD+02 3313 we found a correlation between the measured RVs and one of the stellar activity indicators, suggesting that the observed RV variations may either originate in stellar activity or be caused by the presence of an unresolved companion. We also discuss the current status of the project and a statistical analysis of the RV variations in our sample of target stars. Conclusions. In our sample of 122 solar-mass stars, 49 ± 5% of them appear to be single and 16 ± 3% spectroscopic binaries. The three giants hosting low-mass companions presented in this paper join the six previously identified giants in the sample.