Fully strained single-crystal metastable Ge1-xSnx layers were grown on Ge(001) in order to probe the role of Sn dopant and alloy concentrations (CSn=1×1018cm-3to6.1at.%) on surface roughening pathways leading to epitaxial breakdown during low-temperature (155°C) molecular-beam epitaxy of compressively strained films. The addition of Sn was found to mediate Ge(001) surface morphological evolution through two competing pathways. At very low Sn concentrations (x>~0.02), the dominant effect is a Sn-induced enhancement in both the Ge surface diffusivity and the probability of interlayer mass transport. This, in turn, results in more efficient filling of interisland trenches, and thus delays epitaxial breakdown. In fact, breakdown is not observed at all for Sn concentrations in the doping regime, 1×1018≤CSn≪4.4×1020cm-3(2.3×10-5≤x≪0.010)! At higher concentrations, there is a change in Ge1-xSnx(001) growth kinetics due to a rapid increase in the amount of compressive strain. This leads to a gradual reduction in the film thickness h1(x) corresponding to the onset of breakdown as strain-induced roughening overcomes the surface smoothening effects, and results in an increase in the overall roughening rate. We show that by varying the Sn concentration through the dopant to dilute alloy concentration range during low-temperature Ge(001) growth, we can controllably manipulate the surface roughenin- g pathway, and hence the epitaxial thickness, over a very wide range.