FYI, your score is going to plummet after you go on this app spree. 772 is a very overstated score based on just one CC and a few years of overall history. It will be a while before you get back to 772, but it will be necessary in the long run. I just want you to be prepared for it.
Starting Score: EQ: 665 - TU: 687The inquiry from Chase (or anyone else) hits immediately. And it probably won't have a significant impact if its your first inquiry in a long while. Having a new account (when that hits) will hit you with a new account ding (possibly) and a lowered AAofA ding (possibly).
With your AAofA being a major factor for you currently, I would calculate what your AAofA was before the app (that should be pretty easy in your case 
) and then calculate what it is now with the new account. What numbers do you get? Then calculate again what your AAofA would be with an additional account. Remember that AAofA is always rounded down, and some folks recommend that you avoid doing an app if it would pull you down a year (i.e. if it would bring your AAofA down from 3 to 2; or from 2 to 1).
Depending on your answer, and not having done the math, I might consider waiting 6 months or so before doing another app.
Your current scores are nice and healthy. DH's FICO of 804 (with one open revolving account) was shot down to 760 just with app spree's and lowered AAofA. You can decimate AAofA in a few minutes and it takes years (Iiterally) to build it up again.
DH never received a recommendation from FICO to add accounts. I'm guessing in your case it's because you have a thin file - he didn't. So YMMV.
You may want to wait until the new account hits your reports and then pull your FICO again - see what the estimator then gives you as best steps moving forward.
Hope that's somewhat helpful!
I have never seen a score as high as 772 with such a thin profile, and I'm wondering...
You said you pulled your FICO from Equifax and it was 772, yet credit karma is in the high 600s. That's an awfully large gap, considering that i think the ck score tries to mimic FICO scores. Did you pull your score directly from the EQ website, or from myfico.com?
Awesome advice thanks. I'll see how this new Chase account effects my score before doing any other apps.
I pulled the fico score directly from Equifax. I also thought it was odd that Credit Karma was so far off. FYI, my Credit Karma score used to be in the 750 range, but then I traded in my car and for some reason it plummeted down to 698. I was pleasantly suprised to see my fico score so high.
I would not have a balance on all of them at any time. You should keep a small balance on one or two. I usually just let my daily usage card report whatever the balance is each month and then pay it off after the statement. So, my utilization on the card is usually a little over 10%, but it doesn't really negatively affect my score noticeably, as my total utilization is less than 10%, and I don't think theres a real significant ding until 25% util or so on a single card. Of course, I'm sure this varies like all other FICO scoring factors.
I thought maybe EQ led you to a FAKO, as they do to many now, but that's definitely your FICO score.
Report back what happens to your score once all your new accounts report.