Consider, 

***kick/shift/push/send (something) into overdrive*** [Google Books](https://www.google.fr/search?q=%22the+process+into+overdrive%22&biw=589&bih=386&noj=1&prmd=ivsn&source=lnms&tbm=bks&sa=X&ved=0ahUKEwiwgZTItLHJAhUCOhQKHbo2CjAQ_AUIDCgG)

> into overdrive: into a condition of hard work and effectiveness.
> *There are times when you think this show is going to shift into overdrive, but it never does.* [Cambridge Dictionary of American
> Idioms](http://idioms.thefreedictionary.com/overdrive)

***step up***

> 1. to make something more active. *I hope we can step the pace of business up in the next few days. We can step up business considerably by putting out a larger sign.*
>
> 2. to make something go or run faster. *The engineer stepped the motors up and the production line moved even faster. Please step up the speed of your activity.* [McGraw-Hill Dictionary of American Idioms and Phrasal Verbs](http://idioms.thefreedictionary.com/step+up)

***move/step up a gear***

> to start to work or play more effectively or quickly than before *With
> just five lengths to go, the German swimmer stepped up a gear and
> edged ahead to win the race*. [Cambridge Idioms Dictionary](http://idioms.thefreedictionary.com/step+up+a+gear)

***step on the gas***

> : to hurry in order to get something done quickly; **step on it** *If we're going to get this done today, it's time to step on the gas.*
Etymology: based on the literal meaning of step on the gas (to make a car go faster by giving the engine more gas)
[Cambridge Dictionary of American Idioms](http://idioms.thefreedictionary.com/step+on+the+gas)

***drop the hammer***

> (Expression) American English Idiom: to bring a pending act to
> fruition. Usually connotes an act which will have serious
> consequences. Also used in reference to quickly increasing speed in a
> car by manipulating a manual transmission gear shift (the hammer). [Dictionary Of by Farlex](http://www.definition-of.com/drop+the+hammer)

***(put) the pedal on the metal***

> : to make something go forward or increase as fast as possible : *Ingrid
> put the pedal to the metal and finished writing her essay a day early.*
> Etymology: based on the idea of pressing a car's gas pedal (a flat
> piece that you control with your foot) all the way to the floor to
> make the car go as fast as possible. [Cambridge Dictionary of American Idioms](http://idioms.thefreedictionary.com/Pedal)

***shift to full throttle*** [Google Pictures](https://www.google.fr/search?biw=1024&bih=672&noj=1&tbm=isch&sa=1&ei=CXpYVtzRM8S2af66hZAJ&q=motorcycle+throttle&oq=motorcycle+throttle&gs_l=mobile-gws-serp.1.0.0i19l5.5584.12274.0.13550.18.17.0.1.1.0.2305.7542.0j10j3j7-1j1j1.16.0....0...1c.1.64.mobile-gws-serp..10.8.2602.eV0m473kSl0)

>  The definition of full throttle is doing something at full speed.
An example of full throttle is a runner racing with his optimal energy and speed. [Your Dictionary](http://www.yourdictionary.com/full-throttle#SGLlG0e3mX3QLAA2.99)