High-dimensional entanglement is a valuable resource for secure and efficient quantum information processing. A major challenge for practical use of multidimensional quantum systems is the establishment of controls over arbitrary superposition states in realistic conditions. This work demonstrates spatially entangled photon pairs propagating through two separate four-core optical fibers with the amplitudes and phases of the superposition being independently controllable. Using quantum state analyzers that can detect arbitrary multicore superposition states, Bell-type CGLMP inequalities in two, three, and four dimensions are directly tested. Enhanced violation of the inequality by slight nonmaximality of entanglement is also demonstrated.