  We study the models of Kafri, Taylor and Milburn (KTM) and Tilloy and Di\'osi
(TD), both of which implement gravity between quantum systems through a
continuous measurement and feedback mechanism. The first model is for two
particles, moving in one dimension, where the Newtonian potential is
linearized. The second is applicable to any quantum system, within the context
of Newtonian gravity. We address the issue of how to generalize the KTM model
for an arbitrary finite number of particles. We find that the most
straightforward generalisations are either inconsistent or are ruled out by
experimental evidence. We also show that the TD model does not reduce to the
KTM model under the approximations which define the latter model. We then argue
that under the simplest conditions, the TD model is the only viable
implementation of a full-Newtonian interaction through a continuous measurement
and feedback mechanism.
