There's already a term for this, it's called moonlighting.
Every full-time salaried job I've ever had prohibits moonlighting, and specifically calls it out in the employment contract I've had to sign when starting the job.
Having said that, I am unemployed directly and entirely because of Donald Trump. Although I have no plans to return to work in the immediate future (because I was privileged enough to be in a position where I was able to save for a rainy day like this), when I return to work I am considering doing this.
As long as I'm making my deadlines and producing quality work, my employer should not give a crap whether I have other jobs. Period. I've spent my entire career so far working with bosses that tell me I'm family, but treat me like dirt and discard me at the very first sign of an economic downturn. They are all the same. So, when you treat people like disposable cogs, don't be surprised when and if those cogs fit a variety of different machines.