  Adapter layers are lightweight, learnable units inserted between transformer
layers. Recent work explores using such layers for neural machine translation
(NMT), to adapt pre-trained models to new domains or language pairs, training
only a small set of parameters for each new setting (language pair or domain).
In this work we study the compositionality of language and domain adapters in
the context of Machine Translation. We aim to study, 1) parameter-efficient
adaptation to multiple domains and languages simultaneously (full-resource
scenario) and 2) cross-lingual transfer in domains where parallel data is
unavailable for certain language pairs (partial-resource scenario). We find
that in the partial resource scenario a naive combination of domain-specific
and language-specific adapters often results in `catastrophic forgetting' of
the missing languages. We study other ways to combine the adapters to alleviate
this issue and maximize cross-lingual transfer. With our best adapter
combinations, we obtain improvements of 3-4 BLEU on average for source
languages that do not have in-domain data. For target languages without
in-domain data, we achieve a similar improvement by combining adapters with
back-translation. Supplementary material is available at
https://tinyurl.com/r66stbxj
