  In the context of top-quark condensation models, the top-quark alone is too
light to saturate the correct value of the electroweak scale by its condensate.
Within the seesaw scenario the neutrinos can have their Dirac masses large
enough so that their condensates can provide significant contribution to the
value of the electroweak scale. We address the question of a phenomenological
feasibility of the top-quark and neutrino condensation conspiracy against the
electroweak symmetry. Mandatory is to reproduce the masses of electroweak gauge
bosons, the top-quark mass and the recently observed scalar mass of
$125\,\mathrm{GeV}$ and to satisfy the upper limits on absolute value of active
neutrino masses. To accomplish that we design a reasonably simplified effective
model with two composite Higgs doublets. Additionally, we work with a general
number $N$ of right-handed neutrino flavor triplets participating on the seesaw
mechanism. There are no experimental constraints limiting this number. The
upper limit is set by the model itself. Provided that the condensation scale is
of order $10^{17-18}\,\mathrm{GeV}$ and the number of right-handed neutrinos is
${\cal O}(100-1000)$, the model predicts masses of additional Higgs bosons
below $250\,\mathrm{GeV}$ and a suppression of the top-quark Yukawa coupling to
the $125\,\mathrm{GeV}$ particle at the $\sim60\,%$ level of the Standard model
value.
