The BBP has a targeted offer for 20k MR after $5k/3 months:
https://www.doctorofcredit.com/amer...lus-20000-point-offer-2x-purchases-50000-cap/
There's also a 10k MR offer via "support link" after $3k/3 months. A few people have their links up for the BBP on /r/DISchurners.
The BBP has no annual fee so it makes for a great card to hold MR points, won't report to your personal credit report or count against 5/24, and earns 2x MR on every purchase up to $50k/calendar year.
[ETA: You mentioned you have 4 Amex credit cards. The BBP
is a credit card, so counts against Amex’s limit — I think it’s 5 credit cards now?]
There's some thought, but very mixed DPs, that opening a MR card will reduce your chance of getting targeted for the 100k MR Platinum. I'm not sure if that's true for the BBP. Pretty sure if you open the Premier Rewards Gold ("PRG"), you won't get targeted for the 100k MR Platinum. The PRG was my first Amex card, and I've never received any targeted offers for the 100k MR Platinum, never had any luck triggering 100k, and eventually settled for 75k MR on my first Platinum.
The PRG is a decent card. The public offer is 25k MR, but you can pretty easily use incognito to pull a 50k MR offer after $2k/3 months (best offer is 50k MR after $1k/3 months). It earns 2x MR at restaurants, grocery stores and gas stations, a $100 airline fee credit that's good for a $100 GC from AA or Southwest (or 2x $50 GC from Delta), 3x MR for flights booked directly with airlines, first year AF waived (but $195 AF after that). Bonus categories are nothing spectacular -- especially when the BBP earns 2x MR on everything -- but the card's a moneymaker in its first year with the signup bonus, fee credit, and waived AF. But if you want to hold out for the 100k MR Platinum, or get back under 5/24, you may want to hold off on the PRG.
If you have some big spend coming up, Amex has business versions of their gold and platinum charge cards with big bonuses but high MSRs.
@SouthFayetteFan, any other ideas for
@kmc8826 if she wants to start earning MRs?