The original request for "the strongest rod available" sounds like a code phrase for "I dunno exactly what I want, and there are no specs, but I want it real strong". That sounds bad, and not thought through well, but it may reflect a real situation in which much of the info one might want is just not available.
Usually, when you dig into the back story, you find out that the "rod" is probably not gonna be the limitation. Some other part is really the problem, and the idea behind the "ask" is to shift the failure onto a particular part.
But that may not be the way to do it, because often "very strong" goes along with "breaks right above that stress". The "strongest" part "for the application" may not be the one with the highest ultimate tensile strength, or the one with the highest yield point.
Even 4140 can be quenched and tempered to be over 200,000psi in yield, and at about 250,000 psi ultimate tensile strength. At least my Bethlehem steel book shows that. A 400F temper is given for those results, with just over 1550F as the temp it is quenched from, in oil.
This is the point that the usual question is "Just what do these pins need to do in the assembly? And how do high strength pins help the larger assembly be stronger?"
Those answers may not be available, for various reasons from NDAs to lack of data.
"Pins" typically are used in shear, which can be assumed to be about 40% to 60% of the tensile strength. So presumably the 4140 could be 120k psi in shear, or at 0.0314 sq inch, about 3000 to 3700 lb ultimate in single shear.
Most likely, a person will not do a lot better than that, so that's probably a good maximum design point.