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Did you get the Amex with those charge offs reporting?
The ones that charged off in 2017 are just about ready to fall off the report. You could try a dispute with 'too old to report' being the reason. This will cause the CRA to verify the date of the delinquency with the creditor. It may or may not result in the charge off being dropped off your report now.
I've had mixed results. I had two collections removed six months early. I also had two that had their 'data updated', whatever that means. Looking at the reports side by side I saw no difference between before and after. Those aged off at their 7 year mark.
as for adding new accounts I would wait
most prime issuers want nothing to do with those of us with past charge offs.
a piece of advice I was given early on in my rebuild was 'app for the cards you Want/Need, not the cards you can get'
meaning in the beginning of a rebuild you app for rebuilder cards because you need them to establish positive payment history and usage stats.
after that just tend the garden for however long it takes for all baddies to fall off
Then app for the cards you want
for me it was over two years.
started in the 500s with five collections and a charged off auto loan
now I'm in the 750s because I didn't keep getting cards along the way.
everytime you get a new card you take a hard inq hit and lower your average age of accounts
Im just about ready to start shopping for a new card now
Why not try for some soft pull CLIs on the accounts you already have to pad your uti.
If those are your only negative marks on your reports, and you hold off on opening any new accounts
AND , if you keep up 100% on time payments and your uti low while waiting those charge off out, your scores should jump way past 700 as soon as the last one falls off
I saw a 78 point jump in my fico 8s as soon as my last collection was removed.
When my one charge off dropped off my credit reports last fall, my score jumped up nicely despite still having collections. The monthly reporting and high utilization was really affecting my score. P.S. I did do early exclusion with Transunion, but I think I let the other two drop off on their own time schedule which was at about 7 years.