Hi. I am not aware of any research that undermines the use of multiple approaches to teaching content in a single lesson. On the contrary, I think most people would agree that this is good practice, giving pupils more hooks onto which to hang their learning. By contrast, problems with Learning Styles include the assumption that (a) individuals can only learn well in one way; (b) all content can be taught equally well via all modalities (i.e. Visual, Auditory or Kinaesthetic); and (c) individuals need to be taught in the same way for all subjects. None of this has been found to be true and taking a Learning Styles approach has not been found to predict enhanced progress or achievement. You might find this paper interesting:
Willingham, D. T., Hughes, E. M., & Dobolyi, D. G. (2015). The scientific status of learning styles theories. Teaching of Psychology, 42(3), 266-271.
Consensus for the incorporation of multisensory learning to support learners (learning through engaging more than one sense), is being justified through research on multisensory development. That is learners’ development of sensory neural circuits requires exposure to multisensory experiences. Promising research in museum-based learning is supportive of multisensory learning and also flags up a combination of interactive pedagogic strategies involving the child, museum environment, technology-enhanced learning, peers and/or adults encourages multisensory learning. For a recent review see: Andre, L., Durksen, T., & Volman, M. L. (2017). Museums as avenues of learning for children: A decade of research. Learning Environments Research, 20(1), 47-76. DOI: 10.1007/s10984-016-9222-9
If you want to know more about scientific understandings of multisensory development then, as a start, see the editorial article in Frontiers in Psychology by Monaco et al. (2016), accessed via: https://www.frontiersin.org/articles/10.3389/fnhum.2016.00179/full. The focus is on sense of vision and integration with sense of touch (haptic).
Whilst pedagogy for multi-sensory learning is supported within early years and special education, this may not be always be provisioned for as children get older. This may change as we gain more of an evidence-base of effectiveness of multisensory learning.