Characterization of the dynamics of massive star systems and the astrophysical properties of the interacting components are a prerequisite for understanding their formation and evolution. Optical interferometry at milliarcsecond resolution is a key observing technique for resolving high-mass multiple compact systems. Here we report on VLTI/GRAVITY, Magellan/FIRE, and MPG2.2m/FEROS observations of the late-O/early-B type system HD 93206 A, which is a member of the massive cluster Collinder 228 in the Carina nebula complex. With a total mass of about 90 M_sun, it is one of the most compact massive-quadruple systems known. In addition to measuring the separation and position angle of the outer binary Aa - Ac, we observe BrG and HeI variability in phase with the orbital motion of the two inner binaries. From the differential phases analysis, we conclude that the BrG emission arises from the interaction regions within the components of the individual binaries, which is consistent with previous models for the X-ray emission of the system based on wind-wind interaction. With an average 3-sigma deviation of ~15 deg, we establish an upper limit of p ~ 0.157 mas (0.35 AU) for the size of the BrG line-emitting region. Future interferometric observations with GRAVITY using the 8m UTs will allow us to constrain the line-emitting regions down to angular sizes of 20 uas (0.05 AU at the distance of the Carina nebula).