Chemical recycling of polymers can lead to many different products and play a significant role in the circular economy through the use of plastic waste as a feedstock in the production of valuable materials. The polyolefins: polyethylene (PE) and polypropylene (PP), together with polystyrene (PS), can be chemically recycled by the thermal cracking (pyrolysis) process. In this study, continuous cracking of polyolefins and polystyrene in different proportions and with the addition of other polymers, like polyethylene terephthalate (PET) and polyvinyl chloride (PVC), was investigated at the pilot scale in terms of the process parameters and product yields. Gas chromatography with mass spectrometry (GC-MS) was used for the detailed analysis of the products’ compositions. The boiling temperature distribution and the bromine number were used for additional characterization of products. It was found that an increase of PP share caused a decrease in the process temperature, an increase of the product yield and a shift of the boiling range towards lighter products, increasing the content levels for unsaturates and branched hydrocarbons. It was observed that the addition of 5% PS, PET and PVC reduced the overall product yield, resulting in the creation of a lower-boiling product and increasing the conversion of polyethylene. An addition of 10% polystyrene increased the PP conversion and resulted in a higher product yield, without significant change in the boiling temperatures distribution.