We consider the Brezis-Nirenberg problem in dimension N≥4, in the supercritical case. We prove that if the exponent is close to N+2 N-2 and if, simultaneously, the bifurcation parameter tends to zero at an appropriate rate, then there exist radial solutions which behave like a superposition of bubbles, namely, solutions of the form γ∑ j=1 k 1 1+M j 4/(N-2) |y| 2 (N-2)/2 M j (1+o(1)), γ=(N(N-2)) (N-2)/4 , where M j →+∞ and M j =o(M j+1 ) for all j. These solutions are close to turning points ‘to the right’ of the associated bifurcation diagram.