This paper discusses the potential of immersing foreign language learners in Social Virtual Reality (SVR) in an international seminar, designed by the authors, called SpEakWise VR, combining the tandem language learning paradigm with gamification in immersive virtual environments. SpEakWise VR builds on an existing telecollaboration (SpEakWise) between undergraduate students in Trinity College Dublin and Hildesheim University. We set out to explore how inclusion of an SVR activity influences student engagement, learning involving intercultural and multilingual problem solving, and team building. This paper presents initial observations from our research, concerning multimodality in embodied immersion and code-switching, and proposes future avenues of inquiry. [For the complete volume, "Intelligent CALL, Granular Systems and Learner Data: Short Papers from EUROCALL 2022 (30th, Reykjavik, Iceland, August 17-19, 2022)," see ED624779.]