Oscillatory measurements are often used to explore the nonlinear response of materials, with recently a strong focus on using large amplitude oscillatory experiments. However, the superposition of an oscillatory motion onto a steady-state shear flow is a method where the kinematic history experienced by the sample is simpler. Such a superposed oscillation can be applied either orthogonal or parallel to the main flow direction. Both superposed deformation modes can now be achieved on rotational rheometers equipped with a force-rebalanced transducer, the orthogonal mode requiring a minor modification to the control loop of the normal force. In the present work, the nonlinear properties of a wormlike micellar (WLM) solution are studied. The results are compared with the predictions of the Giesekus model, which is chosen both for its capability to describe the WLM response and for being one of the simplest continuum models that incorporate an anisotropic microstructure. From the fluid response in the homogeneous flow regime, a rate-dependent relaxation time and a rate-dependent plateau modulus can be derived. The latter provides insight into the structural anisotropy during flow at short length scales, which in this case is isotropic. Further analysis of the superposition moduli can be used to separate and quantify the effects of flow on the reptation and breaking of the chains. In the shear-banding regime, the orthogonal moduli show a weaker dependence on shear rate compared to the predictions of the Giesekus model, yet they remain sensitive to changes in the shear-banded state.