Aims. Fast radio bursts are bright radio transients whose origins are not yet understood. The search for a multi-wavelength counterpart of those events can set a tight constraint on the emission mechanism and the progenitor source. Methods. We conducted a multi-wavelength observational campaign on FRB 20180916B between October 2020 and August 2021 over eight activity cycles of the source. Observations were carried out in the radio band by the SRT both at 336 and 1547 MHz and the uGMRT at 400 MHz. Simultaneous observations were conducted by the optical telescopes Asiago (Galileo and Copernico), CMO SAI MSU, CAHA 2.2 m, RTT-150 and TNG, and X/γ-ray detectors on board the AGILE, Insight–HXMT, INTEGRAL, and Swift satellites. Results. We present the detection of 14 new radio bursts detected with the SRT at 336 MHz and seven new bursts with the uGMRT from this source. We provide the deepest prompt upper limits in the optical band for FRB 20180916B to date. In fact, the TNG/SiFAP2 observation simultaneous to a burst detection by uGMRT gives an upper limit E_optical/E_radio < 1.3 × 10². Another burst detected by the SRT at 336 MHz was also co-observed by Insight–HXMT. The non-detection in the X-rays yields an upper limit (1 − 30 keV band) of E_{X − ray}/E_radio in the range of (0.9 − 1.3) × 10⁷, depending on the model that is considered for the X-ray emission.