For the RMn3O6 manganites, we have shown that tuning A-B exchange, by choice of A-site cation or by doping magnetic impurities, gives rise to dramatically different magnetic ground states. We propose an experiment to observe the effect of an alternative tuning mechanism, via B-B exchange. Four different RMn3O6 compounds were synthesised; SmMn3O6 with 25%, 50% and 75% Ti4+ on the B-sites, and a fourth NdMn3O6 sample with 50% Ti4+ on the B sites. All four samples magnetically order, where remarkably an increase in non-magnetic Ti ions increases the ordering temperature. The Ti-doped NdMn3O6 sample features a second phase transition at ~15K, which we hypothesise to be a spin-flop transition based on magnetometry data and point charge calculations. This experiment will form a crucial part of our study on the RMn3O6 compounds and will be paramount in determining their phase diagram.