The extension of advanced tokamak scenarios towards densities close to the Greenwald value is important to demonstrate its reactor relevance. At JET a scenario for high-density Internal Transport Barriers (ITB) has been developed. Plasmas with a reversed magnetic shear were fuelled by pellets, creating a peaked density profile. Additional heating by NBI and ICRH caused a strong internal transport barrier to form in these plasmas. The density and temperature gradients due to the transport barrier cause a large bootstrap current fraction that helps to sustain the shear reversal. Discharges in JET with a negative central magnetic shear often feature temporal collapses of the internal transport barrier that are attributed to double tearing modes. It is known that rotational shear has a stabilising effect on these modes. The high density and consequential low plasma rotation may have a destabilising effect on these modes. The paper addresses the stability of high-density discharges and gives a detailed description of the MHD characteristics and its influence on the plasma rotation.