I know of at least two frameworks other than social semiotics that addressed multimodality. You may want to have a look at the work of Charles Forceville on advertising from the relevance theoretic perspective (i.e. a branch of pragmatics). However, my own work has addressed multimodality from the intercultural (Maalej, 2001, 2003, 2014) and the cognitive metaphor perspective (Maalej, 2015).

If you are interested, you may download my work at:

https://www.researchgate.net/profile/Zouheir_Maalej

https://king-saud.academia.edu/ZouhairMaalej

I hope this will help you.

Halliday defines language as a "social semiotic", because language is a system of signs used in society to fulfill its social functions. SFL thus views language as the most important means of enacting social interaction, language is a "meaning potential".  In this sense SFL is a linguistic theory about language as a social semiotic system, it mainly deals with the interact between grammar/language as a choice system and the functions/meanings (Halliday uses three metafunctions, the ideational ,the interpersonal and the textual functions) that these purposful choices can enable, e.g., to choose among the transitivity systems to enable ideational function, to choose among the mood systems to enable the interpersonal functions, etc. Kress and van Leeuwen's grammar of color and visual design borrows such theoretic constructs as the metafunctions, the grammatical choices such as transitivity, mood and modality, cohesion, etc. We can say that their theory of color and visual design is modeled on Halliday's SFL.  The grammar of color and visual design is nowadays used extensively in multimodal studies of various sorts, such as mentioned in Zouheir's replay, in multimodal metaphor study, to explain how meanings (conceputal and interpersonal) are conveyed and how internal cohesion of various modes of expressions is achieved to contribute to the overall fulfillment of these meanings. 

I may misunderstand the question, but there are several theories on multimodality which do not focus on social aspects or semiotics (e.g. work on the McGurk effect - fusion between audition and vision). One theoretical concept that is not talking explicitly about social semitics is presented here in this paper

http://www.gipsa-lab.grenoble-inp.fr/~jean-luc.schwartz/fichiers_public_JLS/fichiers_pdf/Schwartz_JNL_2010.pdf

Best Susanne

Depending on the type of multimodality you are looking at, there are a range of other approaches. Considering text-image relations, apart from Forceville, a look at the works by Hartmut Stöckl, Ludwig Jäger or Werner Holly might be of interest to you. If you are interested in gesture-speech relations from a linguistic perspective, works by Ellen Fricke, Cornelia Müller or Alan Cienki might be of helpful. A good overview of multimodality research on speech and gesture, also presenting approaches from psychology, semiotics, or anthropology, for instance, is given in the 2 volume handbook "Body-Language-Communication" published by de Gruyter in 2013 and 2014. 

Thank you all for your insightful answers. I think you are right and the term multimodality is being applied by a wide range of fields, with different theoretical approaches. In the Handbook of Multimodal Analysis, edited by Carey Jewitt, I could have a better grasp of the differences between a social semiotic approach and that of systemic functional grammar. They share a lot in common as they all derive from the work of Michael Halliday, but have different emphasis on grammar, on considering the importance of context in the analysis and the role of the sign-maker.

From the perspective of Gregory Ulmer's work Applied Grammatology. Post(e)-Pedagogy from Jacques Derrida to Joseph Beuys (1985), Jacques Derrida's oeuvre constitutes a very concrete demonstration of multimodality. Ulmer argues that Derrida writes with a picto-ideo-phonographic style seeing how he uses "three levels of communication—images, puns, and discourse". From the perspective of Derrida's remark in Of Grammatology about "a peculiarity of our epoch that, at the moment when the phoneticization of writing [...] begins to lay hold on world culture, science, in its advancements, can no longer be satisfied with it", one could say he was announcing multimodality - which from Ulmer's perspective could also be described as a "new Egyptology" - already in this work. Semiotics as a mode, way, style or method of deciphering is as old as the mountains when you come to think of it. Writing in general/cognition has always been a multimodal affair and "today something [just] lets it appear as such, allows it a kind of takeover without our being able to translate this novelty into clear cut notions of mutation, explicitation, accumulation, revolution, or tradition." The mad multitude of descriptions (and applications) of multimodality is thus perhaps not surprising - what is life without the teasing challenge to try and reduce it to meaning? We not for nothing have at least five sense - life (and its possible meaning) remains an art/tekhne to master. Compare also the work of Avital Ronell and Bernard Stiegler, to mention just two of several interesting authors dealing with Derrida's oeuvre. Robert Luke's "Signal Event Context: Trace Technologies of the habit@online" (2004) is also fascinating. As he puts it: "The habit@id:entity is the user proxy that accumulates presence within the habit@online, a constant and consistent mediated representation of the digital self in formation." Perhaps one could say that multimodality gives us today eventually a chance for "living on - borderlines" (cf. Derrida), which of course gives one more (if undecidable in mode) agency than one could have wished for?! When I press "send" here now soon, I will be spacing out in a mode I have no control over ...