  We analyse photometry of $\sim$2000 Galactic Cepheids available in the OGLE Collection of Variable Stars. We analyse both Galactic disk and Galactic bulge fields; stars classified both as single- and multi-periodic. Our goal was to search for additional low-amplitude variability.   We extend the sample of multi-mode radial pulsators by identifying ten new candidates for double-mode and six new candidates for triple-mode pulsation. In the first overtone OGLE sample, we found twelve Cepheids with additional periodicity having period ratio $P_{\rm x}/P_{\rm 1O}\in (0.60,\, 0.65)$. These periodicities do not correspond to any other radial mode. While such variables are abundant in the Magellanic Clouds, only one Cepheid of this class was known in the Galaxy before our analysis. Comparing our sample with the Magellanic Cloud Cepheids we note a systematic shift towards longer pulsation periods for more metal rich Galactic stars. Moreover in eleven stars we find one more type of additional variability, with characteristic frequencies close to half of that reported in the group with (0.60,\, 0.65) period ratios. Two out of the above inventory show simultaneous presence of both signals. Most likely, origin of these signals is connected to excitation of non-radial pulsation modes.   We report three Cepheids with low-amplitude periodic modulation of pulsation: two stars are single-mode fundamental and first overtone Cepheids and one is a double-mode Cepheid pulsating simultaneously in fundamental and in first overtone modes. Only the former mode is modulated. It is a first detection of periodic modulation of pulsation in this type of double-mode Cepheids. 
Frequency analysis of OGLE-IV photometry for classical Cepheids in   Galactic fields: non-radial modes and modulations