Although the requirements for overall recycling rates can only be met when organic recycling is not overlooked, information is scarce regarding adaption to biowaste composting of existing mechanical–biological treatment (MBT) plants originally designed for stabilization of organic municipal solid waste (OFMSW). Thus, this study aimed to assess the suitability of the operational conditions in the biological part of a full-scale MBT plant now used for stabilization of OFMSW (working line: closed-module–covered-pile–open-pile) with a view to producing compost from biowaste. Temperatures above 75 °C were maintained in the closed module and reached again in the covered pile, indicating that intensive organic-matter mineralization occurred in both stages. In the covered pile, the temperature sharply decreased, indicating depletion of easily biodegradable organic matter. An aerobic 4-day respiration test (AT4) value below 10 mg O2/g dry matter, the cut-off for assessing compost stability, was obtained after 8 weeks. However, a high content of humic substances (HS), reflecting compost maturity, was obtained only after 120 days. The increase in HS content proceeded in two phases. In the first phase (45–84 day), the rate constant and the rate of HS formation were lower than in the second phase (84–120 day) (0.072 vs. 0.087 day−1, 1.97 vs. 3.06 mg C/(g organic matter·d)). All the above-mentioned indicators and the nutrient content (N, P, K, Mg, Ca) in the compost indicates that the biological stage of an MBT plant can successfully treat biowaste. This is in accordance with a circular economy and will contribute to increasing recycling rates.