While most of the rare earth metals readily form trihydrides, due to increased stability of the filled 4f electronic shell for Yb(II), only YbH$_{2.67}$, formally corresponding to Yb$^{\rm II}$(Yb$^{\rm III}$H$_4$)$_2$ or Yb$_3$H$_8$, remains the highest hydride of ytterbium. Utilizing diamond anvil cell methodology and synchrotron powder x-ray diffraction we have attempted to push this limit further via hydrogenation of metallic Yb (at room temperature and heated in situ) and of Yb$_3$H$_8$. Compression of the latter has also been investigated in a neutral pressure transmitting medium, PTM. While the in situ heating of Yb facilitates the formation of YbH$_2$ plus x hydride, we have not observed the clear qualitative differences between the systems compressed in H$_2$ and He or Ne PTM. In all these cases a sequence of phase transitions from the unit cells of P-31m symmetry to the I4/m and I4/mmm systems occurred within ca. 13 to 18 GPa and around 27 GPa, respectively. At the same time, the molecular volume of the systems compressed in H$_2$ PTM is ca. 1.5% larger than of those compressed in inert gases, suggesting a small hydrogen uptake. Nevertheless, hydrogenation towards YbH$_3$ is incomplete, and polyhydrides do not form up to the highest pressure studied here of ca. 75 GPa. As pointed out by our electronic transport measurements under compression in NaCl PTM, the mixed-valence Yb$_3$H$_8$ retains its semiconducting character up to at least 50 GPa, although the very low remnant activation energy of conduction, smaller than 5 meV, suggests that the metallization under further compression should be achievable. Finally, we provide a theoretical description of a hypothetical stoichiometric YbH$_3$.