In recent research, additions of solute to Ti and some Ti-based alloys have been employed to produce equiaxed microstructures when processing these materials using additive manufacturing. The present study develops a computational scheme for guiding the selection of such alloying additions, and the minimum amounts required, to effect the columnar to equiaxed microstructural transition. We put forward two physical mechanisms that may produce this transition; the first and more commonly discussed is based on growth restriction factors, and the second on the increased freezing range effected by the alloying addition coupled with the imposed rapid cooling rates associated with AM techniques. We show in the research described here, involving a number of model binary as well as complex multi-component Ti alloys, and the use of two different AM approaches, that the latter mechanism is more reliable regarding prediction of the grain morphology resulting from given solute additions.