  We investigate the blazar contribution to the cumulative neutrino intensity
assuming a generic relationship between neutrino and gamma-ray luminosities,
$L_{\nu}\propto (L_{\rm ph})^{\gamma_{\rm lw}}$. Using the gamma-ray luminosity
functions for blazars including flat spectrum radio quasars (FSRQs) and BL Lac
objects, as well as the $Fermi$-LAT detection efficiency, we estimate
contributions from {blazars resolved by $Fermi$-LAT as well as the unresolved
counterpart.} Combining the existing upper limits from stacking analyses, the
cumulative neutrino flux from all blazars ({including $Fermi$-LAT resolved and
unresolved ones}) are constrained { in the range $0\lesssim\gamma_{\rm
lw}\lesssim2.5$}. We also evaluate the effects of the redshift evolution and
the effective local number densities for each class of FSRQs, BL Lacs, and all
blazars, by which we place another type of constraints on the blazar
contribution using the non-detection of high-energy neutrino multiplets. We
demonstrate that these two upper limits are complementary, and that the joint
consideration of the stacking and multiplet analyses { not only supports the
argument that blazars are disfavored as the dominant sources of the 100-TeV
neutrino background, but it extends this argument by including also
$Fermi$-LAT-unresolved blazars as well, for a more generic luminosity
correlation $L_{\nu}\propto (L_{\rm ph})^{\gamma_{\rm lw}}$}.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology