Our goal is to study the effect of the number of conferencing rounds on the capacity of large interference networks. We do this at hand of the per-user multiplexing gain (MG) of Wyner's soft-handoff model with dedicated conferencing links between neighbouring transmitters and receivers. We present upper and lower bounds on the per-user MG of this network, which depend on the capacities of the transmitter- and receiver-conferencing links and on the number of allowed conferencing rounds. The bounds are tight when: the prelogs of the conferencing links are small or high; there is only transmitter conferencing or only receiver conferencing; or some symmetry conditions between transmitter-conferencing and receiver-conferencing hold. We also determine the per-user MG of the network when the number of conferencing rounds is unlimited. Our results show that for small conferencing prelogs around 1/6, a single conferencing round suffices to attain the maximum per-user MG when the number of conferencing rounds is unconstrained. In contrast, when the prelogs are large, then every additional conferencing round increases the maximum per-user MG.