Of course. You can apply for patent protection for your process improvement. Of course, technology can only apply for invention patents. However, if you are also creative and innovative in processing equipment or tools, you can also apply for a patent for utility model. Because you use other people's principles, after improvement, you process other materials, and the technology used is different from his, which is not within the scope of his patent protection. Through your improvement, you have produced unexpected effects on the processing of other materials. Of course you can apply for a patent.
For his principle, it should be the current technology. You treat it as the existing technology and background technology in the patent specification, and your improvement is the part that your invention should protect. If you want to implement and produce commercial effects, you must get permission from others (patented technology that is valid during the protection period), but he must also get your permission to use your patented technology. If you are both inseparable, you must cross-license to achieve it.