Branching fractions of the decays H b → H c π − π + π − relative to H b → H c π − are presented, where H b ( H c ) represents ¯¯¯ B 0 ( D + ), B − ( D 0 ), ¯¯¯ B 0 s ( D + s ), and Λ 0 b ( Λ + c ). The measurements are performed with the LHCb detector using 35     pb − 1 of data collected at √ s = 7     TeV . The ratios of branching fractions are measured to be [ B ( ¯¯¯ B 0 → D + π − π + π − ) ] / [ B ( ¯¯¯ B 0 → D + π − ) ] = 2.38 ± 0.11 ± 0.21 , [ B ( B − → D 0 π − π + π − ) ] / [ B ( B − → D 0 π − ) ] = 1.27 ± 0.06 ± 0.11 , [ B ( ¯¯¯ B 0 s → D + s π − π + π − ) ] / [ B ( ¯¯¯ B 0 s → D + s π − ) ] = 2.01 ± 0.37 ± 0.20 , [ B ( Λ 0 b → Λ + c π − π + π − ) ] / [ B ( Λ 0 b → Λ + c π − ) ] = 1.43 ± 0.16 ± 0.13 We also report measurements of partial decay rates of these decays to excited charm hadrons. These results are of comparable or higher precision than existing measurements.