Having the rooms offset from the grid- and keep the existing floor also around the room reaching the girders to support it
Having the room offset from the grid "floating" with structural support from new inserted structural elements
Having the room avoid the columns/offset from the columns - get structural support from the girders
Having the room avoiding the whole grid and not go orthogonal in-between the grid but do the opposite.
Conclusion:
The offset of the room whether it only is from the columns or the whole grid (idea 2+3)- that would create light trace from around the room when you see them from underneath.
The last solution has the advantage that the grid will be untouched and the grid will be an independent element and the rooms another element.
The two solution I will work/investigate further is the last two as they have two very different approaches to the grid but the one with the offset around the columns uses the existing structure for structural support of the room and the other makes it possible to make the rooms stand out from the grid and vice versa and also opens up to the possibility of creating more diverse spaces.