Several studies found cross-linguistic structural priming with various language combinations. Here, we investigated the role of two important domains of language variation: case marking and word order, for transitive and ditransitive structures. We varied these features in an artificial language learning paradigm, using three different artificial language versions in a between-subjects design. Priming was assessed between Dutch (no overt case marking, SVO word order) and (a) an SVO order version, (b) a case marking version, and (c) an SOV order version. Similar within-language and cross-linguistic priming was found in all versions for transitives, indicating that cross-linguistic structural priming was not hindered. In contrast, for ditransitives we found similar within-language priming for all versions, but no cross-linguistic priming. The finding that cross-linguistic priming is possible between languages that vary in morphological marking or word order, is compatible with studies showing cross-linguistic priming between natural languages that differ on these dimensions.