Integrability in spectral problem of the planar AdS/CFT is well established during last 17 years. However, the integrable structure is generally lost beyond the planar level. Meanwhile, stacks of giant gravitons in AdS_5 x S^5 are realized by specific LLM geometries which can be drawn by a black disk and concentric black rings on 2D LLM plane. Gauge duals of these new geometries are not just single trace operators and includes contribution of multitrace operators. All those can be conveniently rewritten by a Schur polynomial operator which is represented in terms of a Young diagram. In gravity side, considering stringy excitations on the geometry corresponds to adding small boxes on the Young diagram. This full setup already includes nonplanar diagrams. Nevertheless, one can show that there surprisingly exist integrable subsectors by giving some constraints for excitations in the setup.