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We suggest a new class of tests for searching for lepton flavor non-universality (LFNU) using ratio observables and based on correlations among the underlying LFNU new physics (NP) effects in several (seemingly independent) di-lepton and single lepton + jet(s) processes. This is demonstrated by studying the effects generated by LFNU 4-Fermi interactions involving 3rd generation quarks. We find that the sensitivity to the scale (Λ) of the LFNU 4-Fermi operators significantly improves when the correlations among the various di-lepton +jets and single-lepton + jets processes are used, reaching Λ∼O(10) TeV at the HL-LHC.