  Flavor-universal neutrino self-interaction has been shown to ease the tension
between the values of the Hubble constant measured from early and late Universe
data. We introduce a self-interaction structure that is flavor-specific in the
three active neutrino framework. This is motivated by the stringent constraints
on new secret interactions among electron and muon neutrinos from several
laboratory experiments. Our study indicates the presence of a strongly
interaction mode which implies a late-decoupling of the neutrinos just prior to
matter radiation equality. Using the degeneracy of the coupling strength with
other cosmological parameters, we explain the origin of this new mode as a
result of better fit to certain features in the CMB data. We find that if only
one or two of the three active neutrino flavors are interacting, then the
statistical significance of the strongly-interacting neutrino mode increases
substantially relative to the flavor-universal scenario. However, the central
value of the coupling strength for this interaction mode does not change by any
appreciable amount in the flavor-specific cases. We also briefly analyze a
scenario with more than three neutrino species of which only one is
self-interacting. In none of the cases, we find a large enough Hubble constant
that could resolve the so-called Hubble tension.
