  The main result of this paper establishes that the known Arazy-Cwikel
property holds for classes of uniformly K-monotone spaces in the quasi-Banach
setting provided that the initial couple is mutually closed. As a consequence,
we get that the class of all quasi-Banach K-spaces (i.e., interpolation spaces
which are described by the real K-method) with respect to an arbitrary mutually
closed Banach couple enjoys the Arazy-Cwikel property. Another consequence
complements some previous results by Bykov and Ovchinnikov, showing that this
property holds also for the class of all interpolation quasi-Banach spaces with
respect to a quasi-Banach couple whenever all the couples involved have the
uniform Calder\'{o}n-Mityagin property. We apply these results to some
classical families of spaces.
