  Heavy-quark symmetry as applied to heavy hadron systems implies that their
interactions are independent of their heavy-quark spin (heavy-quark spin
symmetry) and heavy flavour contents (heavy flavour symmetry). In the molecular
hypothesis the $X(3872)$ resonance is a $1^{++}$ $D^*\bar{D}$ bound state. If
this is the case, the application of heavy-quark symmetry to a molecular
$X(3872)$ suggests the existence of a series of partner states, the most
obvious of which is a possible $2^{++}$ $D^*\bar{D}^*$ bound state for which
the two-body potential is identical to that of the $1^{++}$ $D^*\bar{D}$
system, the reason being that these two heavy hadron-antihadron states have
identical light-spin content. As already discussed in the literature this leads
to the prediction of a partner state at $4012\,{\rm MeV}$, at least in the
absence of other dynamical effects which might affect the location of this
molecule. However the prediction of further heavy-quark symmetry partners
cannot be done solely on the basis of symmetry and requires additional
information. We propose to use the one boson exchange model to fill this gap,
in which case we will be able to predict or discard the existence of other
partner states. Besides the isoscalar $2^{++}$ $D^*\bar{D}^*$ bound state, we
correctly reproduce the location and quantum numbers of the isovector
hidden-bottom $Z_b(10610)$ and $Z_b(10650)$ molecular candidates. We also
predict the hidden-bottom $1^{++}$ $B^*\bar{B}^*$ and $2^{++}$ $B^*\bar{B}^*$
partners of the $X(3872)$, in agreement with previous theoretical speculations,
plus a series of other states. The isoscalar, doubly charmed $1^+$ $D D^*$ and
$D^* D^*$ molecules and their doubly bottomed counterparts are likely to bind,
providing a few instances of explicitly exotic systems.
