I know there was a previous thread where I read about this, but I couldn't find it when I did a search. My time is limited as today is re-sign your free agents day.

I have a guy who I traded for last season that is a stud hitter. The previous owner gave him a mutual option for the final year of his contract (I thought I would be ok to stick around as he has 72 Patience.) but he has decided to opt out.
Now I would like to re-sign him as I have the option to offer him contracts despite the fact that he claims he is going free agency no matter what. I remember seeing someone being able to resign their guy for some percentage over their demands. His asking salary is 3 years at $7,833,333 per season. My first attempt with $3M extra per year failed and my next attempt of $4M extra per season will be processed in the next hour.
I do not want to lose this guy for what will probably amount to a 1* and 2nd or 3rd round pick as he is annually good for around .350 BA, .420 OBP, and .550 SLG.

I'm pretty sure the "going FA no matter what" guys will never re-sign in the sign your own FA period.  It's the "unless you surprise me with a great offer" guys that might sign for an offer somewhere above their asking amount.

I once offered a "going FA no matter what" guy the max contract and he rejected it in the sign your own FA period.

I think you're looking for this thread, but keep in mind that you probably won't re-sign him if he's filing for free agency no matter what. The guy I was able to re-sign said, "Unless you really surprise me with a great offer, I'm filing for free agency."

That said, I found that a 50 percent increase over his initial asking price (with a mutual option in the last year) did the trick. Your $4 million increase should be enough, if he's at all interested in returning.

What's his patience rating, btw? If it's below ~60, you're probably screwed.

His patience rating is actually 72, but my $4M was not enough. So it seems that I am out of luck.

just keep submitting it and maybe you'll get lucky.

Add another year?

I wouldn't go too nuts with the details.  It's possible that he'll reject one offer, and sign a same or lesser one later.

In my experience, that guy is gone. Of course, you'll still have the opportunity to bid for him in the FA period, but it sounds like he's gonna be awfully expensive. You should get 'A'  type comp, though, if he signs with someone else.