I prefer "intercultural" to "cross-cultural" because it sound more multilateral. Perhaps "transcultural" is better. I suspect that some term codification has been established in someone's research.
• Multicultural communication supposes the coexistence of several cultures.
• Intercultural communication suggests interactions between different cultures.
• Intercultural communication necessarily concerns situations of contact.
• Transcultural communication can be defined as communication which are valid across social groups, or which do not take into account cultural differences.
Even if I like the answer by Nebi, in my experience, there is no stable definition of those concepts - every actor defines them in another way, many times not making a clear difference between them. I came across Catherine Walsh who tries to distinguish interculturality, multiculturality and pluriculturality - interesting but far from binding. Unfortunately, I can't find the text...
Although I agree that there is no consensus among experts, one distinction that makes perfect sense to me is that "intercultural" can be used to refer to contacts (communicative and otherwise) between different cultures or members of those cultures, while "cross-cultural" can be used to refer to the various ways in which people of different cultures communicate (or do something else) within their own cultures. This is analogous to the practice of many who study generational communication, who often use "intergenerational" to refer to communication between members of different generations (e.g., grandparent-grandchild communication) and "cross-generational" to refer to the comparison and contrast between communication within different generations (e.g., how teenagers communicate with their peers as compared to how the elderly communicate with their peers).
Admittedly like most social constructs, the terms multicultural, cross-cultural intercultural and transcultural are open to interpretations and a range of definitions depending when, where, how and what. Have you considered Bhabha's 1994 - The location of culture. there's a lot of food for thought in this text starting with the concept of culture and developing its evolution into the various forms and representations.
One aspect which is perhaps missing from the terms inter and cross cultural which may be implicit in the term transcultural is the idea of tranformation and transition. The terms inter and cross culturality or communication seem to assume that participants and their culture remain unchanged by their experience in communicating with individuals from different backgrounds to their own. In reality, or at least, in my experience, interactions of this type have developed, altered and transformed personal culture. Similarly, there may also be an assumption, with the terms inter and/or cross culturality that the cultures of each participant are reified and unchanging. In today's globalised society, culture and identity could be considered as fluid and in flux therefore, potentially making it unrealistic to assume that any one "culture" is fixed. Personally, I prefer the term transcultural as it is less rigid, allows for each participant to have a complex and fluid culture which can be influenced, developed and transformed through interaction with individuals with other equally complex cultural backgrounds
Brock -- I know that this is an old question, but I have recently heard the concept of "meta-cultural communication." This refers to not just across cultures, or between cultures, but rather the ability to interact successfully with any other culture.
The paper linked below defines "Meta-cultural competence" is "a competence that enables interlocutors to communicate and negotiate their cultural conceptualizations during the process of intercultural communication’."
Chapter Developing Meta-cultural Competence in Teaching English as a...