  Considering our (3+1)-dimensional space-time as, in some way, discrete or l
attice with a parameter $a=\lambda_P$, where $\lambda_P$ is the Planck length,
we have investigated the additional contributions of lattice artifact monopoles
to beta-functions of the renormalisation group equations for the running fine
structure constants $\alpha_i(\mu)$ (i=1,2,3 correspond to the U(1), SU(2) and
SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group
Model (FRGGM) which is an extension of the Standard Model at high energies. It
was shown that monopoles have $N_{fam}$ times smaller magnetic charge in FRGGM
than in SM ($N_{fam}$ is the number of families in FRGGM). We have estimated al
so the enlargement of a number of fermions in FRGGM leading to the suppression
of the asymptotic freedom in the non-Abelian theory. We have shown that, in
contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at
$\mu=\mu_G\sim 10^{18}$ GeV, we have the possibility of unification if the
FRGGM-breakdown occurs at $\mu_G\sim 10^{14}$ GeV. By numerical calculations we
obtained an example of the unification of all gauge interactions (including
gravity) at the scale $\mu_{GUT}\approx 10^{18.4}$ GeV. We discussed the
possibility of $[SU(5)]^3$ or $[SO(10)]^3$ (SUSY or not SUSY) unifications.
