  The notion of mid $p$-summable sequences was introduced by Karn and Sinha in
2014 and recently explored and expanded by Botelho, Campos and Santos in 2017.
In this paper we design a theory of mid summable sequences in the anisotropic
setting defining a new more general space called space of mid $(q,p)$-summable
sequences. As a particular case of our results, we prove an inclusion relation
between spaces of mid summable sequences. We also define classes of operators
that deals with this new space, the mid $(q,p)$-summing operators, and prove
some important results on these classes as inclusion and coincidence theorems
and a Pietsch Domination-type theorem. It is worth to mentioning that these
abovementioned results are new even in the particular case of the mid
$p$-summable environment.
