Trans-Neptunian binaries are among the objects carrying the most relevant information on the conditions that prevailed in the primitive outer Solar system. However, their present orbital architecture not necessarily reflects those conditions, because it is the result of complex evolutionary processes. There is evidence suggesting that binary systems dominated the primitive trans-Neptunian populations. Therefore, binary–binary interactions could be an important evolutionary path. In this paper, a series of numerical experiments of binary–binary close encounters were carried out, varying specific parameters related to their physical and orbital characteristics. The relative speeds with which the encounters occur play an important role in the relative variation of orbital elements, showing a good agreement with impulsive approximation models involving a binary and a single intruder. However, simulations varying the mass, semimajor axis, and closest approach distance between pairs of binaries, showed marked deviations from this model.