Concerns about the depletion of petroleum reserves and rising pollution led researchers to search for alternate and environmentally compatible fuels for compression ignition engines. As an excellent alternative fuel additive to biodiesel–diesel blends, higher alcohol exhibits outstanding fuel properties (such as high energy content and cetane number) and can operate in diesel engines without requiring engine changes. This study focuses on investigating the ternary blends comprising higher alcohols, namely 1-heptanol and n-octanol, in hybrid biodiesel (animal fat oil–rice bran oil–cottonseed oil) and diesel on compression ignition engine characteristics. The performance, combustion, and emissions of a diesel engine fuelled with mono (D100), binary (B20), and ternary fuel blends (B20H10, B20H20, B20O10, and B20O20) were analysed at a constant engine speed of 1500 rpm. The test fuels met the American Society for Testing and Materials standards for fuel properties and exhibited stable behaviour during testing. Experimental results showed that at 100% load, the least brake-specific fuel consumptions for diesel fuel, B20, B20H10, B20H20, B20O10, and B20O20 were 254.1 g/kWh, 302.14 g/kWh, 281.25 g/kWh, 310.94 g/kWh, 292.8 g/kWh, and 313.80 g/kWh, respectively. Meanwhile, the maximum brake thermal efficiency values were obtained as 38.65%, 37.01%, 37.76%, 36.84%, 37.12%, and 36.38%, respectively. At 100% load, the peak heat release rates for diesel, B20, B20H10, B20H20, B20O10, and B20O20 were found to be 64.65 J/deg, 59.07 J/deg, 62.34 J/deg, 56.12 J/deg, 57.95 J/deg, and 51.9 J/deg, respectively. The addition of 1-heptanol and n-octanol as oxygenated additives into the ternary blend resulted in decreased carbon monoxide and unburned hydrocarbon emissions while increasing carbon dioxide and nitrous oxide emissions compared to diesel fuel. Overall, the study concludes that ternary blends with 1-heptanol and n-octanol as additives improve performance and combustion behaviour and reduce exhaust emissions compared to binary blends.