Yes, you can. Standard store-bought probiotics can be a valuable addition for many people. However, the question is whether they fit your specific situation.
Not only the bacterial species is important, but also the bacterial strain. Different strains within the same species can have different properties and therefore give a different effect.
For example, Lactiplantibacillus plantarum WCFS1 and Lactiplantibacillus plantarum KLH1 belong to the same bacterial species, but they are different strains with different properties.
When a practitioner chooses a specific strain of bacteria, this is done on the basis of your analysis, complaints and medical situation. Therefore, you cannot automatically assume that another strain of the same species will have the same effect.
In addition, within a personal microbiome treatment, bacterial strains and ingredients can also be used that are not or only only to a limited extent available through stores or webshops.