Keep Our Pension Promises Act This bill repeals the elimination of the pension anti-cutback provisions under the Multiemployer Pension Reform Act of 2014. The anti-cutback provisions prohibit reductions in pension benefits to participants in multiemployer pension plans. The bill amends the Employee Retirement Income Security Act of 1974 (ERISA) to allow a plan sponsor of an eligible multiemployer plan to petition the Pension Benefit Guaranty Corporation for a partition of a financially-troubled pension plan. PBGC is required to establish a legacy fund to cover the administrative and benefit costs resulting from a partition.. The bill amends the federal bankruptcy code to assign first claim priority to pension obligations under ERISA. The bill amends the Internal Revenue Code to: