We suggest a new CPX-derived scenario for the search of strangephilic MSSM Higgs bosons at the Tevatron and the LHC, in which all neutral and charged Higgs bosons decay predominantly into pairs of strange quarks and into a strange and a charm quark, respectively. The proposed scenario is realized within a particular region of the MSSM parameter space and requires large values of tan(beta), where threshold radiative corrections are significant to render the effective strange-quark Yukawa coupling dominant. Experimental searches for neutral Higgs bosons based on the identification of b-quark jets or tau leptons may miss a strangephilic Higgs boson and its existence could be inferred indirectly by searching for hadronically decaying charged Higgs bosons. Potential strategies and experimental challenges to search for strangephilic Higgs bosons at the Tevatron and the LHC are discussed.