  Self-focusing instability is a well-known phenomenon of nonlinear optics,
which is of great importance in the field of laser-plasma interactions.
Self-focusing instability leads to beam focusing and, consequently, breakup
into multiple laser filaments. The majority of applications tend to avoid the
laser filamentation regime due to its detrimental role on laser spot profile
and peak intensity. In our work, using nonlinear Schr\"{o}dinger equation
solver and particle-in-cell simulations, we address the problem of interaction
of multiple parallel beams in plasmas. We consider both non-relativistic and
moderately relativistic regimes, and demonstrate how the physics of parallel
beam interaction transitions from the familiar self- and mutual-focusing
instabilities in the non-relativistic regime to moderately relativistic regime,
where an analytical description of filament interaction is impenetrable.
