Using multireference configuration interaction expansions comprised of over 7 million configuration state functions, three-state conical intersections are reported for the closely spaced, spectroscopically observed B((2)A(1)), C(B-2(1)), and D(B-2(2)) states (in C-2v symmetry) of the allyl radical. These conical intersections of states which were previously assigned as the 3,4,5(2)A states and are here reassigned as the 4,5,6(2)A states, are expected to be accessible using optical probes. This conclusion is obtained from the structure of the minimum energy point on the 4,5,6(2)A three-state conical intersection seam which is similar to the equilibrium structure of the ground X((2)A(2)) State and only 1.1 eV above the D(B-2(2)) state at its equilibrium geometry. The seam of three-state degeneracies joins two two-state seams of conical intersection, the 4,5(2)A and 5,6(2)A conical intersection seams. The energy of the minimum energy point on the 4,5(2)A two-state seam is only 0.15 eV above that of the D(B-2(2)) state at its equilibrium structure. Three-state intersections are also reported for the 3,4,5(2)A states.