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.
Exercises
SUNG part (upper): four steady quarter notes — the basic pulse. Vocalize as "one, two, three, four" or "da, da, da, da." PLAYED part: a basic backbeat — hi-hat 8ths in your hand (not notated above; play them), kick on 1 and 3, snare on 2 and 4. The sung quarters land WITH every kick and snare, so this is the easiest version. The point is to wire the singing-and-playing pathway.
SUNG part (upper): a syncopated 8th-note melody — hits on 1, & of 2, 3, & of 3, & of 4, with rests in between. PLAYED part: the basic backbeat (kick 1 and 3, snare 2 and 4 — add hi-hat 8ths in your hand). Now the voice and the snare hand DON'T line up. The voice has its own line; the limbs have theirs. If you find yourself unconsciously playing what you sing, stop, breathe, and start again — the voice has to live separate from the hand.
SUNG part (upper): 8th-note triplets with an ACCENT on every third note — i.e., a 3-against-4 cross-pulse, "ONE-two-three, ONE-two-three, ONE-two-three, ONE-two-three." Sing only the accented notes if it helps: "ONE...ONE...ONE...ONE..." evenly spaced, four times per bar. PLAYED part: kick on 1 and 3 only — hands free, no hi-hat or snare. The voice is in 3 (a waltz-like grouping); the foot is in 4. They line up only on beat 1. This is your first taste of cross-meter — and the technique that lets you handle it is singing.
SUNG part (upper): steady quarter notes — the same pulse-sing as Ex 1. PLAYED part: a syncopated kick figure on 1, & of 2, 3, & of 4. The sung pulse and the kick syncopation only line up on 1 and 3. The technique here flips: the voice now holds the steady pulse while the limbs do the syncopation. This is how Chester recommends practicing every reading exercise — sing the pulse so the limbs can read freely.