I will start out by stating a few things to diffuse possible objections. One thing to keep in mind is that there is an infinite difference between a grace based salvation, and salvation by grace ALONE. When we reject the idea of salvation by grace alone, we are not rejecting grace altogether.
I also wish to short-circuit accusations of creating a straw man argument that is easy to defeat. There are a significant number of conservative / fundamental / Calvinist / Evangelical type Christians who explicitly proclaim a salvation that is by grace alone, and will question the Christianity of anyone who believes otherwise.
Further, I will state that my motivation here is to clear the way for reasonable discussion about salvation with fellow Christians. Once we get beyond a claim of salvation by grace alone, it is then a matter of discussing what criteria there is for salvation, rather than whether there is any criteria whatsoever.
So with that, I would like to present my simple attempt at a logical argument against salvation by grace alone:
P1: Salvation is not Universal (there will be some souls who are not saved).
P2: Salvation is not entirely random.
C: Salvation by Grace Alone must be rejected.
It is likely that someone will say that there is a better way to formulate the above, but I hope it will communicate the argument sufficiently. If there is anyone who is not saved, and if this is not random, then there must be some criteria for salvation, which is not grace alone. Or put another way, for those who claim salvation is by grace alone, they must either accept that salvation is universal, or that salvation is random. I see no way out of this. Let me know if you feel I am missing something here.