First, Google’s TOS (Terms of Service) states that they do not allow you to
have more than one account. That rule needs to be explained further
however. If you have two or more accounts with the purpose of trying to
dominate the sponsored searches (called double serving) so that those
who click end up on sites that are duplicates of each other, that is definitely
not allowed. In fact, you are likely to be found out and permanently banned.
If however, you have two accounts but they are used for two sites selling vastly different things, there is no problem at all. However, there really is no reason to have separate accounts for separate sites. You can do all your advertising for all sites from one account.
As for the specific question, one type of “mess” you hear is that if your QS is low, there is no way out and you must start from scratch. There is NO “mess” that cannot be fixed. Quality Score is low? It can be improved and quite rapidly too with some effort.
Another similar theme that some suggest is that you have to dump your domain and get a new one. Somehow, they believe that the domain is cursed. There are some instances of domains being what is called slapped. This slapping is actually a flagging of the domain for doing things Google considers detrimental to its users, such as installing malicious software. Google doesn’t index that domain for organic rankings and doesn’t allow advertising to it as well.
I’m assuming none of you are malicious. A low QS very likely has nothing to do with being slapped for the above. It is simply because you are not doing things right. No need to get a new domain or new account. Simply fix the problem.
What is really amazing is that those who cling to this messy account myth suggest copying the account to another and copying the domain to a new one. Without making any sort of change. They expect that the Adwords routines will somehow disregard the way it calculated their score before. If you simply copy, you will get the same results. Guaranteed. Searchers are not any more likely to click the same ad now when they didn’t before.