From Oxford Advanced Learner's Dictionary, there is the following example sentence for the second meaning in the entry of the noun profile.
We first build up a detailed profile of our customers and their requirements.
I feel a detailed profile in that sentence reads a little weird. I think it has to be modified into the plural form detailed profiles since they will be multiple ones as the customers would be more than one.
But as that sentence is from a prominent dictionary, there will be no way it would be wrong. What do you think about that?