  We explore the bounds that can be placed on interactions between cold dark
matter and vacuum energy, with equation of state $w=-1$, using state-of-the-art
cosmological observations. We consider linear perturbations about a simple
background model where the energy transfer per Hubble time, $Q/H$, is a general
linear function of the dark matter density, $\rho_c$, and vacuum energy, $V$.
We explain the parameter degeneracies found when fitting cosmic microwave
background (CMB) anisotropies alone, and show how these are broken by the
addition of supernovae data, baryon acoustic oscillations (BAO) and
redshift-space distortions (RSD). In particular, care must be taken when
relating redshift-space distortions to the growth of structure in the presence
of non-zero energy transfer. Interactions in the dark sector can alleviate the
tensions between low-redshift measurements of the Hubble parameter, $H_0$, or
weak-lensing, $S_8$, and the values inferred from CMB data. However these
tensions return when we include constraints from supernova and BAO-RSD
datasets. In the general linear interaction model we show that, while it is
possible to relax both the Hubble and weak-lensing tensions simultaneously, the
reduction in these tensions is modest (reduced to less slightly than $4\sigma$
and $2\sigma$ respectively).
