Chris Allen Multiemployer Pension Recapitalization and Reform Act of 2021 This bill makes various changes with respect to the administration of multiemployer pension plans. Among other provisions, the bill allows qualified multiemployer plans to apply for special partition assistance from the Pension Benefit Guaranty Corporation (PBGC). Partition assistance generally authorizes the PBGC to take financial responsibility for a portion of the liabilities of a plan at risk of insolvency. Subject to certain exceptions and conditions, special partition assistance expands eligibility for partition assistance and does not require plans to repay the amount of assistance received. The bill also revises the PBGC rules for determining whether a plan is insolvent and the procedures for terminating a plan that fails to meet certain standards. Additionally, the bill sets forth the discount rates used to estimate a plan's future benefit payment obligations, which affect an employer's minimum contribution to the plan. It also establishes a stable funding status and an unrestricted funding status and revises the criteria for plans that are in endangered, critical, and critical and declining statuses. Finally, the bill establishes rules for new composite plans. Composite plans provide annuity benefits to plan participants, establish fixed contributions from employers, and require realignment measures if the plan's projected funded ratio falls below 120%. A composite plan's projected funded ratio is the actuarial projection of the plan's assets compared to liabilities as of the first plan day of the 15th plan year following a given plan year.