  We study regularity issues for systems of elliptic equations of the type \[
  -\Delta u_i=f_{i,\beta}(x)-\beta \sum_{j\neq i} a_{ij} u_i
|u_i|^{p-1}|u_j|^{p+1} \] set in domains $\Omega \subset \mathbb{R}^N$, for $N
\geq 1$. The paper is devoted to the derivation of $\mathcal{C}^{0,\alpha}$
estimates that are uniform in the competition parameter $\beta > 0$, as well as
to the regularity of the limiting free-boundary problem obtained for $\beta \to
+ \infty$.
  The main novelty of the problem under consideration resides in the
non-trivial grouping of the densities: in particular, we assume that the
interaction parameters $a_{ij}$ are only non-negative, and thus may vanish for
specific couples $(i,j)$. As a main consequence, in the limit $\beta \to
+\infty$, densities do not segregate pairwise in general, but are grouped in
classes which, in turn, form a mutually disjoint partition. Moreover, with
respect to the literature, we consider more general forcing terms,
sign-changing solutions, and an arbitrary $p>0$. In addition, we present a
regularity theory of the emerging free-boundary, defined by the interface among
different segregated groups.
  These equations are very common in the study of Bose-Einstein condensates and
are of key importance for the analysis of optimal partition problems related to
high order eigenvalues.
