Typing 110-120 wpm, your fingers are hitting ~10 characters per second which is a pretty impressive feat if you think about it; most people will never be able to achieve much beyond that, even with dedication & practice.
One thing you can do is ensure you have a decent keyboard that you're comfortable & familiar with. I'd recommend a mechanical keyboard with Cherry MX brown switches (light tactile feedback without the annoying 'click' of blue switches) - but ultimately, keyboards are highly subjective.
The fastest typists these days swear by Colemak-DH which just like Workman fixes many of the shortcomings of Colemak.
To me Workman feels the best, but anything that's not QWERTY is measurably better, whereas the difference between Colemak, Dvorak and so on is more circumstantial.
There's a 2-3 second timeout to motivate you to type fast. Also, it pulls words from the buffer you have open, so you can practice on a set of words that you use regularly. It starts with short words and gradually moves to longer and more complex words to see if you can keep up.
Of course, it will only teach you Dvorak, but then again, you did say that you wanted to type faster...