Essentially you are describing one of the biggest notional failures of how the steel buildings were being constructed in Spain till the early 70's. They had columns with battens, and inside the pair of the simple members constituting the column a short stub of double tee or channel, or worse, even on the battens, continuous beams were supported. Essentially, so, a gravity system. In the best cases (most fortunately by the seventies') a 3 plane system of bracing was added, but in the cases that not, it was the masonry itself -and floor system, sometimes just laid unattached on the beams- what was providing for stability and whatever bracing available. Essentially they were replicating ways of the past, where no clear assignment of the structural function was given to the components; most reform works' parties were and are unaware of the proper functionality and it is one of the causes of accidents happening at such works.
In all, for the worse cases, what supported was complementing the ability of what supporting to provide the expected functionality. Exactly like in your case. Anytime that I have been practicing, and now by the code in the final report for the construction, the works that need to be kept untouched as components of the structural safety and integrity must be identified in the document and postmarked in-situ.