The incorrectly named 'middle tunning needle' isn't just a needle is really a modification of the position of the low-end needle and the spray bar on the venturi (who is the too called 'little brass screw').
To start playing with the location of the low-end needle you need to have a grasp of how works the carburetors in our engines and what provide if you modify the shape of the end (the one that plugs on the spray bar), their lenght and their position relative to the carb venturi.
Some time ago I posted how they worked, just take a look to the post:
Don't think that I'm lazy to write another time, just only wanted to direct you to a post where was explained just along some other commonly mislooked parts on our engines.
Basically modifying the spray bar (if your carburetor allows it) in fact, you're modifying the point in the throttle opening where the fuel flow is dictated by the low-end needle (when plugged completely or partial) or is mandated by the adjustment of the high speed needle.
Playing with the position on the venturi and the lenght of the needle, you're modifying the mid-rpms and how the engine will be (all the engine at part throttle are slightly leaned, this is why isn't recommended to stay lots of time at part throttle).
Do a read, look your carburetor and of course, understand how they work before engaging into the carb modification. is a matter of where the very small details enter into play.