IMO the 'issue' being overlooked is WHY the score currently so low?
It's NOT the difference between 3 vs 4 CCs
Is there a balance being reported on more than one card, a balance of 'any' size....
Any installer TL history?
Secured card, Unsecured card etc is red herring stuff at this point ( given, there are already 3 revolvers already reporting) we're chasing trees in the forest....contemplating as to the 'value' of adding yet another CC as an important swing issue here.
= Barking up, the wrong 🌲
There is something, amiss with the current profile...that has nothing to do with one 'more' card...
Frankly, a person can have a much higher score with LESS cards, so it isn't about 'one' more... especially, when the goal is a mortgage within less than a year on the horizon.
What does the overall reported debt load on the credit report 'look' like?
It's Fool's Gold to think the simple adding of one 'more' CC will fix what is 'hurting' the profile...we constantly forget credit scoring = RISK scoring
What's risky 'looking' enough to have the profile tagged at 640?
Again, it's about what's ON the report, currently, not about dumping funds in some account to add a secured card.
Perhaps that cash may be better spent, cleaning up some bruises appearing ON the current report.
OP stated, "I have a few very small collections accounts I'm starting to pay off and have been current with all my payments for the past 1.5 years (Student loans, credit cards)."
Data point - I did a product change at Cap1 to QuickSilver - same card number, same account age, plus cash back! Nothing but win.