It would be helpful sometimes to be able to pick up one item from a stack, probably by holding a bindable modifier and clicking with a bindable mouse button. I suggest left control or left alt by default. Or it could be set just to middle click, which i don't think does anything in Mouse Tweaks now.

That makes sense. Would a server+client side version or server side addon mod with features like this be practical?

Yeah, though I have no experience with client+server mods. I'm fairly sure I've seen some mods do this kind of functionality.

Since mouse tweaks is client-side only, it has to do its features by more or less emulating mouse clicks. If I'm not mistaken, picking up a single item would mean right clicking to pick up half, then a ton of right clicks to put all but one item back into the stack. I suspect this kind of click spam will not work well, especially on servers.