It is totally OK to ask a bartender to modify a drink for you, as long as that modification is a modification and not a request to create a completely different drink. Just as a chef would get annoyed if you turned their pasta dish with clams into a chicken sandwich, so too would a bartender become disgruntled if your modifications resulted in a completely different cocktail that you should have just ordered in the first place.
That said, modifications do happen often, and most bartenders roll with them quite easily. Perhaps you’re allergic or sensitive to one of the cocktail’s ingredients; simply ask if the cocktail could be made without it or replaced with something else. Or if the base spirit isn’t one you fancy — perhaps it utilizes gin and you like tequila — ask if the drink can be made with your preferred spirit instead and how the bartender thinks it might taste. This is particularly easy if the drink is more of a classic, like a Negroni, and you’d like the bartender to use mezcal instead of gin, for example.
It’s worth noting that if you choose to modify the drink, it’s not a great look to then complain that you don’t like it, or to send it back. While modifications can result in drinks that are just as delicious as the original, by changing the recipe, you’re taking the risk that the drink won’t be as good as the one the bartender or bar created.
Finally, try to keep your modifications to one ingredient if you can. If you can’t, you might want to peruse the menu for a different drink or order a classic cocktail that you know you already like.