A clarifying shampoo is formulated to remove, better than a regular shampoo, the residues that are left on the hair by continuous application of leave-on products or other rinse-off products (e.g., if you want to try a shampoo of a new brand, you can perceive better the results that this new product will give to your hair if, before using the new shampoo, you use a clarifying shampoo to help remove residues of previous products).
It’s important to understand that the benefit of cleaning your hair deeper is given by a mix of ingredients inside your clarifying shampoo, not by a single ingredient. So, adding vinegar to your regular shampoo won’t turn it into a clarifying shampoo.
Besides that, when a shampoo is formulated, many tests are done to guarantee that it delivers the promised benefits, as well as to guarantee an adequate performance of the product until its expiration date. You can check the main steps to create a hair care product on my Free Ultimate Hair Care Product Creation Checklist. If you add a different ingredient (e.g. vinegar) to your regular shampoo, the performance of the product can’t be guaranteed anymore.
PS: Based on the explanation above, if you still would like to test the effect of the addition of an ingredient to your shampoo (due to a curiosity on testing a new combination, as mentioned to the vinegar), avoid losing your entire shampoo bottle. For that, never add any ingredient directly to the original bottle. Instead, put a small quantity of the regular product in another recipient and mix before trying it in your hair.