Most coordination problems are mental, not physical. The limbs already can do four different things; what they can't do is hold four different things in conscious working memory simultaneously. The trick is to outsource one of the parts to a place that's not your hands or feet — your voice.
This is the heart of Gary Chester's The New Breed system: sing an ostinato (a fixed repeating figure) while your limbs play other parts. Once a sung melody is automatic, it stops competing with the limbs for attention; the limbs are free to read, improvise, or comp. Chester built an entire 200-page book around eleven sung melodies — but the technique is older, and you can use it on day one.
What follows are three exercises in escalating singing-vs-playing difficulty. The notation in each shows two voices: the upper line (snare-line note positions) is the SUNG part — it's not played; it's vocalized aloud. The lower line is the kit part. Sing comfortably, on any pitch; pitch isn't the point, rhythm is. Hum, scat, "doo-bah," whatever lets you hold a steady line without thinking about it.
Important: the upper voice is what you SING, not what you play with your hands. Your hands play whatever is in the lower voice (along with whatever the kit pattern requires). Read each exercise's tip to be sure which is which.