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Do you have any needs for credit in the next year or two? E.g. a car loan or a home loan? If so, when?
With respect to the secured card in your name, make a small purchase each month, let it report on the next statement, and then pay that amount in full a few days after the statement prints. Then do it again. The amount that reports should be under 8.99% of the credit limit. So in your case less than $27.
In the case of the AU card, would the owner of the account be willing to keep the reported balance much lower? That would help his score and yours. We can explain how he could spend a lot on the Discover card while keeping his reported balance very low (or even zero).
Do you have any lates, collections, charegeoffs, any other derogs like that?
Have you pulled your three FICO 8 scores? You can do that for a buck at Credit Check Total.
In the case of the AU card, would the owner of the account be willing to keep the reported balance much lower? That would help his score and yours. We can explain how he could spend a lot on the Discover card while keeping his reported balance very low (or even zero).
Good news regarding regarding the card on which you are an AU (the Discover). That person needs to pay it zero as soon as he comfortably can. That move will help both of you a lot.
An important test you should engage in as his balance begins to come down is to pay the only card in your name (a secured card) to zero. If your score drops it means that FICO 8 is not counting that AU card in its scoring. It is very important to know whether FICO 8 is counting it or now.
Regarding your most recent question, I would wait until his balance is getting lower (which I think you believe will happen soon). While you are waiting, research your options to find a secured card which has no annual fee and which also has a good chance of the issuer "graduating" it to an unsecured card.
In general I lean toward getting yourself equipped with 2-3 no annual fee cards as a higher priority than attempting to pay off collections or other bad debts.
Here's how I'd think about it. You can:
(a) Pay off all bad debts first and then add a card.
(b) Add a card and then pay off all debts.
I don't think (A) will get your report clean any faster (partly because you may be unable to negotiate Pay For Delete agreements).
But with (A) when your second card finally appears it has no history or age, whereas with (B) it does. Just do your best to find a card that can graduate to unsecured and which has no fees. That way you'll be able to keep that tradeline open forever.
And of course, stop applying for credit aside from the extra secured card. The 60+ inquiries on your report is crazy high.
PS. Why is it that you don't know how many inquiries are in your EX report? If you have not pulled your EX report you should head over to creditscore.com -- which will give you a free EX report and FICO 8 every month.