The problem of oceanic gap-traversing boundary currents, such as the Kuroshio current crossing the Luzon Strait or the Gulf Stream traversing the mouth of the Gulf of Mexico, is considered. Systems such as these are known to admit two dominant states: leaping across the gap or penetrating into the gap forming a loop current. Which state the system will assume and when transitions between states will occur are open problems. Sheremet (J. Phys. Oceanogr., vol. 31, 2001, pp. 1247–1259) proposed, based on idealized barotropic numerical results, that variation in the current’s inertia is responsible for these transitions and that the system admits multiple states. Generalized versions of these results have been confirmed by barotropic rotating-table experiments (Sheremet & Kuehl, J. Phys. Oceanogr., vol. 37, 2007, 1488–1495; Kuehl & Sheremet,J. Mar. Res., vol. 67, 2009, pp. 25–42). However, the typical structure of oceanic boundary currents, such as the Gulf Stream or Kuroshio, consists of an upper-layer intensified flow riding atop a weakly circulating lower layer. To more accurately address this oceanic situation, the present work extends the above findings by considering two-layer rotating table experiments. The flow is driven by pumping water through sponges and vertical seals, creating a Sverdrup interior circulation in the upper layer which impinges on a ridge where a boundary current is formed. The $\beta $ effect is incorporated in both layers by a sloping rigid lid as well as a sloping bottom and the flow is visualized with the particle image velocimetry method. The experimental set-up is found to produce boundary currents consistent with theory. The existence of multiple states and hysteresis, characterized by a cusp topology of solutions, is found to be robust to stratification and various properties of the two-layer system are explored.