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An inexpensive and high-performing solid Coumarone resin was added to Styrene-butadiene-styrene (SBS) copolymer-modified asphalt to enhance its storage stability and road performance. To assess the effect of Coumarone resin dosage on the SBS-modified asphalt, a series of laboratory tests were conducted. The composite modified asphalt’s segregation test was used to evaluate its storage stability, Dynamic Shear Rheometer (DSR) and Multiple Stress Creep Recovery (MSCR) tests were employed to investigate its high-temperature performance and permanent deformation resistance, and the Bending Beam Rheology (BBR) test was utilized to measure its low-temperature performance. Fluorescence microscopy was used to observe the composite modified asphalt’s microstructure, and Fourier Transform Infrared Spectroscopy (FTIR) was conducted to study the changes in chemical structure during the modification process. The results showed that Coumarone resin can improve the compatibility of SBS and asphalt, improve the high-temperature performance and deformation resistance of SBS-modified asphalt, and adding an appropriate amount of Coumarone resin can help enhance the low-temperature cracking resistance of modified asphalt. The optimal dosage of Coumarone resin recommended for SBS-modified asphalt performance enhancement is 2% under the test conditions, as determined by comparing the test results of samples with various dosages.