The District of Columbia Code Title 42 Chapter 32 Section 11 authorizes a landlord to be able to pursue the following types of monetary judgment during ejectment proceedings:
Claims for Arrears of Rent, Double Rent, and Waste
In either case the landlord may join with his claim for recovery of the possession of the leased premises a claim for all arrears of rent accrued to the termination of the tenancy, and, when the tenant has given the notice, for double rent from the termination of the tenancy to the verdict, or judgment, if the trial be by the court and for damages for waste; provided, that in such action before the Superior Court of the District of Columbia the amount so claimed shall be within its jurisdiction. If judgment for possession be rendered in favor of the plaintiff, he shall be entitled, at the same time, to a judgment for said arrears of rent, and for said double rent, as the case may be, to the date of the verdict or judgment as aforesaid, and for damages for waste.
DC Code § 42–3211.
See also DC How to Serve a Notice to Quit.