Recent scientific research suggests that consumption of 1.2-1.6g of protein per kilogram of body weight per day is an appropriate protein target (1). For example, if your current weight is 80kg then your dietary protein requirements are between 96-128g per day. However, for many elite athletes and competitive bodybuilders (and those competitively striving towards this level), protein needs may be even higher during peak season. In this case, the protein recommendations have been suggested as high as 2.3-3.1g/kg/d to maximise the retention of lean body mass in resistance-trained individuals during hypocaloric periods i.e. low/restricted overall energy intake (2).
A person's individual requirements and current diet will need to be assessed in order to determine how many protein shakes you should be consuming. Protein should come from whole food sources like meat, fish, dairy, seeds, beans and so on first. Protein shakes can then be used to supplement your diet. One protein shake per day, or after each workout, is usually adequate, or up to three servings per day as required.
(1) Noakes, M, (2018) Protein Balance: New Concepts for Protein in Weight Management; CSIRO, Australia.
(2) Jäger R, Kerksick CM, Campbell BI, et al. International Society of Sports Nutrition Position Stand: protein and exercise. Journal of the International Society of Sports Nutrition. 2017;14:20. doi:10.1186/s12970-017-0177-8.