Feedback in the form of outflows is believed to be a key ingredient in galaxy evolution. In cosmic noon galaxies, outflows have mostly been detected - and extensively studied - in the ionised gas phase, only to reveal that ionised gas outflows alone cannot be responsible for the quenching of star formation through mass ejection. It has therefore been surmised that a large fraction of outflowing mass may be in molecular gas form, as suggested by results of luminous but rare AGNs and quasars. To gain insights into the prevalence and impact of molecular gas outflows on galaxy evolution as a whole, we searched for the telltale broad velocity signature in CO line emission, capitalising on the IRAM/PHIBSS CO survey of 175 typical main-sequence massive star-forming galaxies at redshift between 0.5 and 2.6. We use spectral stacking techniques to reach SNRs of 20 and above for the full sample and various physically-motivated subsets. The results suggest that - if present - the molecular gas outflow signature is remarkably weak. We will discuss implications on molecular gas outflow properties, on galaxy evolution, and on future observational work on feedback through outflows at cosmic noon.