  We mainly construct and analyze the multi elliptic-localized solutions under
the background of elliptic function solutions for the focusing modified
Korteweg-de Vries (mKdV) equation. Based on the Darboux-B\"{a}cklund
transformation, we provide a uniform expression for these solutions by the
Jacobi theta functions. The asymptotic behaviors of multi elliptic-localized
solutions are provided directly in two categories. By the consistent asymptotic
expression of those solutions, we obtain that the collisions between the
elliptic-breathers/solitons are elastic. Moreover, a sufficient condition of
the strictly elastic collision between the solitons and breathers has been
given by the symmetric analysis. In addition, as $k\rightarrow0^{+}$, the multi
elliptic-localized solutions degenerate into solitons, breathers or
soliton-breather solutions, which implies that we extend the solutions from the
constant and vanishing backgrounds to the periodic solutions backgrounds.
Moreover, we illustrate figures of the multi elliptic-localized solutions to
visualize the above analysis.
