  In this paper we study a zero-flux attraction-repulsion
che\-mo\-taxis-system. We show that despite any mutual interplay between the
repulsive and attractive coefficients from the corresponding
chemo-sensitivities, even less any restriction on their own sizes, if the
production rate of that chemical signal responsible of the cellular coalescence
is sublinear, then any initial data emanate a unique global classical solution,
which is as well bounded. Further, in a remark of the manuscript, we also
address an open question given in \cite{Viglialoro2019RepulsionAttraction}.
