The short answer is NO, unless there is a very good reason for it.
The long answer includes explanations as to why the answer is usually NO.
Aftermarket or over-the-counter (OTC) oil additives come in a few general variations:
There may be others but a vast majority of them fall into one of these categories.
Performance additives generally include anti-wear, extreme pressure, friction modifying, or nonsense additives. They often have some root in traditional oil formulations; meaning they are commonly used in oil formulating and advertised as “performance boosters”. For the most part, they are unpredictable and the marketing claims for their performance is rarely supported by any credible evidence and usually don’t live up to the expectations.
A big problem is, more rarely equals better for these additives, and simply adding them does not increase their advertised properties. Many of these additives experience diminishing returns with regard to performance and their proportion of the lubricant formula. Other groups of them actually experience decreased performance with increased concentrations.
Another problem with these additives is that they are very surface active chemicals and they often can disrupt the surface activity the original lubricant was designed to do. So by adding one of these chemicals, it is likely to diminish the original performance of the lubricant and substitute it with a less effective replacement.
There are undoubtedly anecdotes of these additives doing good, but that is typically due to luck, because every oil formula is different and adding these random amount of random additives is unpredictable at best without knowing the original oil formulation and exactly what you are adding at what quantity.
One final thing is the “nonsense” additives. Such as PTFE and lots of “nano” additives. These are overwhelmingly ineffective and sometimes detrimental to performance. The claims by the “manufacturers” (usually marketers, not chemical manufacturers) are very lofty, usually unproven, and typically backed up by lots of buzz words and little substance in any technical sense.
Viscosity modifiers are typically either high viscosity oil or a polymeric fluid. They are usually unadditized and therefore dilute the original lubricant’s additive concentration. This is bad for similar reasons stated above. By changing the formula concentrations, you may be changing performance aspects that were balanced in the original formula to an unbalanced concentration. These additives can be useful in a few circumstances though. They can be temporary fixes to compression issues and leaks, but even in fixing those problems, you may introduce unintended consequences such as engine efficiency and oil supply through the sump. If it is the only way to get the vehicle somewhere for maintenance, it might be the best option, but still not good for normal use.
Cleaners come in two varieties: detergent/dispersant additives and flushing compounds. Detergents/dispersants are similar to the performance additives in the sense that they are very surface active and can disrupt the surface active additives in the original oil to its detriment. Detergents, dispersants, anti-wear, and friction modifiers are carefully balanced in oil formulas and increasing the detergent concentration can prevent those other additives from bonding to the metal surfaces where they normally would.
Flushing compounds are usually some sort of high solvency fluid meant to dissolve sludge and carbon deposits in dirty engines. These can be useful in very dirty engines as long as care is taken not to overdo it. If an engine has a high level of sludge and deposits, it is possible to release too much all at once and cause unintended harm by blocking oil flow or forcing that carbon into areas it can do harm.
Inhibitors usually take the form of antioxidants. These are safer than some other additives because they aren’t generally surface active chemicals, but they do still dilute the overall additive concentration and can possibly throw off the balance of a formula to produce worse overall performance. There is less risk in using these types, but still your typical oil has more than enough antioxidant additives in it to begin with and there is rarely a need for more to be added.
Thank you @SuperSalad for this write up. These questions come up frequently in automotive/fuel discussions.