I have a few question to give you a meaningful response:
What was her behavior during the last affair, when she was caught?
Have you ever been for marriage counseling?
If I haer you correctly, the issue is essentially how to approacher? Are you not also interested in the whys?
You were transferred to relationship so I will be helping you with your question. If you feel that you have evidence of your spouse cheating though not red-handed, but the amount of evidence you've dug up over the past little while is overwhelming, hopefully, you've managed to maintain a little sanity during the evidence gathering because the next hurdle will be the biggest yet which will be the confrontation. Confronting a cheating spouse is an all or nothing deal. Once those words are out of your mouth, there is no going back. You need to be sure beyond a shadow of a doubt. In order to do that, you need to have overwhelming evidence.
There are many things that can happen when you accuse your spouse of cheating - denial, anger, sadness, disbelief are among the most common reactions. It is vital that you maintain your composure and be strong after you confront your spouse and let them know that this type of behavior has to stop or it could be the end of your relationship, that is why it's important for you to stay calm or else you will lose what you want to say and then it just turns into a blow up fight and could end in one or the other leaving mad. If you want the marriage to work then you are going to have say it in a way that doesn't sound like you want an end to the marriage. Once exposed, she will likely do anything to turn the tables and make it look like you are the one with the problem like you said and could backfire and make you look like a jealous, delusional, raving lunatic. For this reason, it is best to say what you have to say, just stating the facts, and what you have found and don't listen to any excuses or manipulation attempts, just tell her that the proof is there and that you want to know what she wants to do from here, if she knows you won't listen to excuses she may be apt to tell you what has happened and how far it has gone.
Avoid the urge to tell all your evidence during the confrontation. Don't let her know exactly how much you know, or how you got your proof. You should keep her guessing. Should you decide to forgive your spouse and stay together, you will want to keep those techniques secret as a future deterrent. If they know how you got your info, they will know what not to do if they cheat again. I would also suggest some type of marriage counseling for you both and also for her to get her own type of counseling to find out why she continues to cheat, it could be something that happened in her childhood or something that happened in a past relationship perhaps someone had cheated on her several times and she figures that she would do it first before it is done to her. The most important thing is to find out the root of the reason that she continues to cheat and then come up with some things that will help her to have self control so that the indiscretion doesn't happen again.