A novel concept for a compact high-field magnet coil is introduced. This is based on stacking slit annular discs cut from bulk (RE)BCO ceramic in a Bitter-like architecture. Finite-element modelling shows that a small 20-turn stack (with a total coil volume of <20 cm3) is capable of generating a central bore magnetic field of >2 T at 77 K and >20 T at 30 K. Unlike resistive Bitter magnets, the HTS Bitter stack exhibits significant non-linear field behaviour during current ramping, caused by current filling proceeding from the inner radius outwards in each HTS layer. Practical proof-of-concept for this architecture was then demonstrated through fabricating an uninsulated 4-turn prototype coil stack and operating this at 77 K. A maximum central field of 0.382 T was measured at 1.2 kA, with an accompanying 6.1 W of internal heat dissipation within the coil. Strong magnetic hysteresis behaviour was observed within the prototype coil, with ≈30% of the maximum central field still remaining trapped 45 min after the current had been removed. The coil was thermally stable during a 15 min hold at 1 kA, and survived thermal cycling to room temperature without noticeable deterioration in performance. A final test-to-destruction of the coil showed that the limiting weak point in the stack was growth-sector boundaries present in the original (RE)BCO bulk.