Yes, depending on what you classify medieval weapon. Now your easiest option is to just scale it up. This was actually done with the above Chinese design. Making it larger increased its power. It also becomes to heavy to carry but you didn't specifically list that as a requirement.
The Greeks had a similar siege crossbow, the polybolos. Both could be made much stronger when made out of metal. This would mean they need to be operated by more then one person. But a large crank operated by two or three guys would get you far. But these aren't mobile, at least by a single person.
If you want the mobility of a regular crossbow something gotta give. You either get reduced but respectable power or move further and further from non-explosive but also non-medieval technology. The limitation with handheld systems is that the draw weight needs to be low enough to be done quickly for the next shot, that's in opposition with the strong draw of an arbalest.
Easiest way around this? Cheat. By using motors and electricity. This would give you the power you need to draw a heavier bow while keeping it small enough to be carried by one man. But I doubt this is what you want.
Now you could compromise and go for something like a stirrup and belt hook. The system used the muscles of standing up to load the crossbow. The string was hooked to the belt and a foot in a stirrup kept the bow down. Simply standing up armed it. This system is much stronger then a repeating crossbow as it's not the hand but the entire back and legs pulling the string.
But this will be nowhere near a true arbalest. However if you create a system that allowed standing up to load but is magazine fed you get a decent compromise I think. It can fire as fast as you can squat, which is a pretty decent rate of fire. Compound crossbows also severely lower the required draw weight and combined with some modern materials could give you an improvement.
Now if that's not good enough I really do think you need to power it with something that's not muscle.