Are there known compounds of caesium with oxidation number >1?
As noted in the answer to the other question, alkali metal can exist in higher oxidation state when bonded with polycylic multidendate ligands like cryptands etc. This is an excerpt from an eBook:


  The chemistry of group 1 elements have been dominated by +1 oxidation
  states. However, there have been indications that caesium might form
  higher oxidation species. Thus, electrochemical oxidation of
  $\ce{[CsL]PF6}$ L=18-crown-6 or cryptand-[222] gives evidence for
  $\ce{Cs^2+}$ and $\ce{Cs^3+}$. Compounds containing caesium in higher
  oxidation state is yet to be isolated.


Also, compounds of form $\ce{CsF_n}$ is known to contain stoichiometric amount of caesium in higher oxidation state($\ce{Cs^2+,Cs^3+,Cs^4+,Cs^5+}$). Experimental calculations have confirmed the presence.(See here and here).

Furthermore, it has also been observed by Moock and Seepelt, Angew, Chem. Intl. Ed. Engl. 28, 1676(1989) that $\ce{Cs+}$ can be oxidised in acetonitrile solution to $\ce{Cs^3+}$ at a potential of +3.0 V($\ce{E°}$). - (See this eBook)