For example, how could I have a water pump pour water (inflow) into an existing pool of water (fluid)?
I know that this video: https://www.youtube.com/watch?v=qaaMaWazr1E does not show exactly what you seek, but his method is amazing, and I think it could be adapted to what you are trying for a very realistic result.
His "pool" is a plane on which he uses Dynamic Paint and the Wave system in the modifiers tab to "paint" the splash of his particles on that plane.
If you try to follow along with his video, I suggest you watch it, first, then follow along in Blender, because he shows several things that don't work, in order to explain why, and then show the correct way.
However, even with that, he makes a mistake that totally messes up the final results, by deleting his first dynamic plane. When I recreated this, I, instead, used a second, and left the original for later use. You'll see.
However, there is another way, that might better suit your purposes.
Within your fluid domain, where you want your pool, make an object that fits the size of your pool, and, while assigning the fluid parameters, set that object in the Physics tab with a "Volume Initialization" of "Volume". Assign the same material as you would your "Fluid Domain" material, so they don't contrast. (Or, better yet, at first, make them different, so you can see the effect, then make them the same for your final renders.)
That frame is the very first frame in my example where the new fluid hits the existing pool, so you can see that there is an immediate interaction.
Um, I'm still new at this, so I wasn't sure how to upload my .Blend file for you to examine. I hope the images help you see that it does work.