A method for pyrolyzing a mixed polyolefin feed, comprising: exposing a feedstock comprising a mixture of polyolefins comprising two or more types of monomers to polyolefin pyrolysis conditions to form a pyrolysis effluent, the polyolefin pyrolysis conditions comprising: heating the feedstock at a rate of 100°C per second or more to form a heated reaction mixture having a temperature of 500°C to 900°C, and cooling the heated reaction mixture to a temperature of less than 500°C to form the pyrolysis effluent, the heated reaction mixture being at a temperature of 500°C or more for 0.1 seconds to 5.0 seconds; performing an initial separation on the pyrolysis effluent to form at least a pyrolysis product fraction and a fraction comprising solid particles; performing steam cracking on a steam cracker feed to form a steam cracker reactor effluent, wherein the steam cracker feed comprises whole and partial crudes, naphtha boiling feeds, distillate boiling range feeds, atmospheric resid boiling range feeds, vacuum resid boiling range feeds, or combinations thereof, and is separate from the mixed polyolefin feed; passing at least a portion of the steam cracker reactor effluent into a primary fractionator to form at least a first fractionator product and one or more additional fractionator products having a higher boiling range than the first fractionator product; passing at least a portion of the first fractionator product and at least a portion of the pyrolysis product fraction into a process gas compressor to form a compressed olefin product fraction, a volume of the pyrolysis product fraction comprising 0.1 vol% to 20 vol% of a combined volume in the process gas compressor of the at least a portion of the first fractionator product and the pyrolysis product fraction; and separating at least a first product stream comprising ethylene and a second product stream comprising propylene from the compressed olefin product fraction. heating the feedstock at a rate of 100°C per second or more to form a heated reaction mixture having a temperature of 500°C to 900°C, and cooling the heated reaction mixture to a temperature of less than 500°C to form the pyrolysis effluent, the heated reaction mixture being at a temperature of 500°C or more for 0.1 seconds to 5.0 seconds; performing an initial separation on the pyrolysis effluent to form at least a pyrolysis product fraction and a fraction comprising solid particles; performing steam cracking on a steam cracker feed to form a steam cracker reactor effluent, wherein the steam cracker feed comprises whole and partial crudes, naphtha boiling feeds, distillate boiling range feeds, atmospheric resid boiling range feeds, vacuum resid boiling range feeds, or combinations thereof, and is separate from the mixed polyolefin feed; passing at least a portion of the steam cracker reactor effluent into a primary fractionator to form at least a first fractionator product and one or more additional fractionator products having a higher boiling range than the first fractionator product; passing at least a portion of the first fractionator product and at least a portion of the pyrolysis product fraction into a process gas compressor to form a compressed olefin product fraction, a volume of the pyrolysis product fraction comprising 0.1 vol% to 20 vol% of a combined volume in the process gas compressor of the at least a portion of the first fractionator product and the pyrolysis product fraction; and separating at least a first product stream comprising ethylene and a second product stream comprising propylene from the compressed olefin product fraction. <EOS>