Rhymes with 'downstream'
Scots Language Rhymes
deem
            (Scots for dame, observed in NE)
fleem
        (Scots for phlegm)
Scottish-English Rhymes
beam
                cream
                deem
                dream
                gleam
                meme
                ream
                scheme
                scream
                seam
                seem
                steam
                stream
                team
                teem
                theme
                downstream
                esteem
                extreme
                redeem
                regime
                supreme
                upstream
                self-esteem
Imperfect Rhymes for 'downstream'
Consonant-shift to /in/
94 near rhymes such as bean, been, gene, queen, hygiene, latrine
Consonant-shift to /imd/
17 near rhymes such as creamed, schemed, teemed