We study a Maxwell-CP(2) model coupled to a real scalar field through a dielectric function multiplying the Maxwell term. In such a context, we look for first-order rotationally symmetric solitons by means of the Bogomol'nyi-Prasad-Sommerfield (BPS) algorithm, i.e., by minimizing the total energy of the effective model. We perform our investigation by choosing an explicit form of the dielectric function. The numerical solutions show regular vortices whose shapes dramatically differ from their canonical counterparts. We can understood such differences as characterizing the existence of an internal structure.