  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.
