The ILC baseline consists of two interaction regions, one with a 20mrad crossing angle and the other with a 2mrad crossing angle. It is known that the outgoing beam losses in the final doublet and subsequent extraction line are larger in the 2mrad than in the 20mrad layout. In this work, we exploit NbTi and Nb$_3$Sn superconducting magnet technologies to redesign and optimise the final doublet, with the aim of providing satisfactory outgoing disrupted beam power losses in this region. We present three new final doublet layouts, specifically optimised for the 500 GeV and the 1 TeV machines.