If you are assaulted at a bar, can you also sue the bar as well as the person who assaulted you?

Yes, if the bar overserved the patron, or provided inadequate supervision at the time of the assault.
Be careful, when suing a bar, there are typically shortened statute of limitations.

Well, yes you CAN sue the bar. But the real question is whether and to what extent you have a valid claim that will prevail.

While you CAN sue the bar, the statutes and the case law in most states invoke many protections for liquor licensees. You must prove that they were on notice that the person that they served was intoxicated. This can be done either by direct testimony from witnesseses or by an expert.

But, think about it. Who are the witnesses? Are there any stone cold sober people who were sitting there who can testify with accuracy as to the fact that the assaulter was exhibiting signs of intoxication when they were served a drink by the bar? Lacking direct testimony in this area, then you need expert testimony from a toxicologist or other person knowledgeable enough about blood alcohol to take the BAC when the assaulter was tested after the incident, and then through a process known as reverse interpolation, figure what the BAC would have been when the person was served their last drink AND whether it is more likely than not that with that BAC they would have demonstrated obvious signs of intoxication. That is what is required to demonstrate that the bar served the person when they knew or should have known that the person was intoxicated.

Yes, you can sue the bar. But, the real quesiton is, in view of the many complexities of these cases, only a few of which I've summarized above, whether you have a claim that is likely enough to be a winner to justify the cost in time, effort and money.

You can sue a bird for flying overhead. But, putting aside issues of service, what is the likelihood for success?

This answer is provided for informational purposes only. True legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction and with experience in the area of law in which your concern lies.