This is a Phase Ib/II study with the primary purpose of the Phase Ib part being to estimate the MTD and/or recommended phase 2 dose (RP2D) of the combination of LGH447 and BYL719 when administered orally to adult patients with relapsed and refractory multiple myeloma. Once the MTD and/or RP2D is determined for the combination of LGH447 and BYL719, additional patients will be enrolled in the Phase II part to determine whether the combination of LGH447 and BYL719 exhibits improved anti-multiple myeloma activity compared to single agent LGH447.