We explore the consequences of heavy flavour, heavy quark spin and heavy antiquark-diquark symmetries for hadronic molecules within an effective field theory framework.. Owing to heavy antiquark-diquark symmetry, the doubly heavy baryons have approximately the same light-quark structure as the heavy antimesons. As a consequence, the existence of a heavy meson-antimeson molecule implies the possibility of a partner composed of a heavy meson and a doubly-heavy baryon. In this regard, the Dbar D* molecular nature of the X(3872) will hint at the existence of several baryonic partners with isospin I=0 and J^P = 5/2^- or 3/2^-. Moreover, if the Zb(10650) turns out to be a B*bar B* bound state, we can be confident of the existence of Xibb* bar B* hadronic molecules with quantum numbers I(J^P) = 1(1/2^-) and I(J^P) = 1(3/2^-). These states are of special interest since they can be considered to be triply-heavy pentaquarks.