Vries (mKdV) equation [@AbMu2], [@AbMu3], [@GurPek2]-[@ma], nonlocal real or complex sine-Gordon equation [@AbMu2], [@AbMu3], [@aflm], nonlocal Fordy-Kulish equations [@GurPek3], [@GursesFK], nonlocal $N$-wave systems [@gerd2], nonlocal multidimensional versions of NLS [@fok]-[@gerd3], and so on. The relations between local and nonlocal reductions are given in [@Vincent], [@Yang].

In this work, we consider the coupled Hirota-Iwao modified Korteweg-de Vries (HI-mKdV) system [@IHT], [@IH] $$\label{generaleqn}
\displaystyle \mu v_{i,t}+3(\sum_{j,k=1}^N c_{jk}v_jv_k)v_{i,x}+v_{i,xxx}=0$$ for $i=1, 2, \ldots, N$ where $c_{jk}=c_{kj}$. Here we will study a type of (\[generaleqn\]) given by $$\label{coupledmKdVN}
\displaystyle \mu v_{i,t}+3\rho v_{i,x}+v_{i,xxx}=0, \quad i=1, 2,\ldots, N,$$ where $$\label{rho}
\rho=\sum_{j, k=1, \ldots, N } c_{jk}v_jv_k,$$ and $\mu$ is a constant. Here $c_{jk}=c_{kj}$ and $c_{jj}=0$. We examine all local and nonlocal reductions of HI-mKdV systems (\[coupledmKdVN\]) for any $N$ and present their soliton solutions expressed by pfaffians. We study all possible reductions and give one-soliton solutions of the HI-mKdV systems (\[coupledmKdVN\]) for $N=2, 4$. From the system (\[coupledmKdVN\]) for $N=4$, by using the Ablowitz-Mussilimani type reductions we obtain local and nonlocal systems of two equations. For $N=3$, we give local and nonlocal reductions, and one-soliton solution of (\[coupledmKdVN\]) in Appendix. For this case we also have reductions to systems of two equations, but if we require one-soliton 