Tertiary-level English medium instruction (EMI) presents an opportunity for both EMI and science, technology, engineering and maths (STEM) pedagogies: tertiary STEM needs student-centred strategies familiar to EFL, whereas tertiary EFL can harness the innate complexity of STEM towards complex language production. With the aim of achieving coequal EFL-STEM collaborations, this article presents: (1) neuroscience findings demonstrating the shortcomings of teacher-centred lecturing common in tertiary STEM instruction, and thus the need for EFL expertise; (2) a schema which, by logically delineating the 'language dilemma of content instruction', positions language instruction within STEM education; (3) two grids for guiding instructional design--a two-dimensional grid that disentangles content from language, delineating the cognitive demands imposed by each and helping experts optimize the trajectory of instructional-tasks, and a three-dimensional translanguaging grid delineating all linguistic codes within the EMI space, allowing each EFL-STEM team member to participate in designing student-centred translanguaging tasks without leaving their respective comfort zones; (4) examples of EMI-STEM translanguaging tasks informed by the grids and which guarantee level-appropriate content instruction while supporting the mastery of disciplinary discourses, in both English and the L1.