  The $DK$ interaction is strong enough to form a bound state, the
$D_{s0}^*(2317)$. This in turn begs the question of whether there are bound
states composed of several charmed mesons and a kaon. Previous calculations
indicate that the three-body $DDK$ system is probably bound, where the quantum
numbers are $J^P = 0^{-}$, $I=\tfrac{1}{2}$, $S = 1$ and $C = 2$. The minimum
quark content of this state is $cc\bar{q}\bar{s}$ with $q=u,d$, which means
that, if discovered, it will be an explicitly exotic tetraquark. In the present
work. we apply the Gaussian Expansion Method to study the $DDDK$ system and
show that it binds as well. The existence of these three and four body states
is rather robust with respect to the $DD$ interaction and subleading (chiral)
corrections to the $DK$ interaction. If these states exist, it is quite likely
that their heavy quark symmetry counterparts exist as well. These three-body
$DDK$ and four-body $DDDK$ molecular states could be viewed as counterparts of
atomic nuclei, which are clusters of nucleons bound by the residual strong
force, or chemical molecules, which are clusters of atoms bound by the residual
electromagnetic interaction.
