Clean biofuels are a helpful tool to comply with strict emission standards. The co-processing approach seems to be a compromise solution, allowing the processing of partially bio-based feedstock by utilizing existing units, overcoming the need for high investment in new infrastructures. We performed a model co-processing experiment using vacuum gas oil (VGO) mixed with different contents (0%, 30%, 50%, 70%, 90%, and 100%) of rapeseed oil (RSO), utilizing a nickel–tungsten sulfide catalyst supported on acid-modified phonolite. The experiments were performed using a fixed-bed flow reactor at 420 °C, a hydrogen pressure of 18 MPa, and a weight hourly space velocity (WHSV) of 3 h−1. Surprisingly, the catalyst stayed active despite rising oxygen levels in the feedstock. In the liquid products, the raw diesel (180–360 °C) and jet fuel (120–290 °C) fraction concentrations increased together with increasing RSO share in the feedstock. The sulfur content was lower than 200 ppm for all the products collected using feedstocks with an RSO share of up to 50%. However, for all the products gained from the feedstock with an RSO share of ≥50%, the sulfur level was above the threshold of 200 ppm. The catalyst shifted its functionality from hydrodesulfurization to (hydro)decarboxylation when there was a higher ratio of RSO than VGO content in the feedstock, which seems to be confirmed by gas analysis where increased CO2 content was found after the change to feedstocks containing 50% or more RSO. According to the results, NiW/acid-modified phonolite is a suitable catalyst for the processing of feedstocks with high triglyceride content.