Turbulence generated by an oscillating grid in a two-layer stably stratified system is a classical flow utilized to study various aspects of turbulence in presence of stratification without mean shear. This flow evolves in a quasisteady state, in which the layer thickness and density difference evolves in a quasisteady manner due to the large separation of timescales between the turbulence and the setup. We present an extension of the classical setup that enables full steady state conditions and in which the entrainment velocity can be prescribed separately from the Richardson number. We develop a theoretical box-model and show that the model is in good agreement with the experiments. The model allows to predict the transient response of the system for a variety of initial conditions and the imposed steady state. The new setup is necessary to obtain the steady position of the density interface, for example, when using advanced optical techniques to measure the small-scale features of turbulence near the interface.