I have the BCP and have my eye on the SPG card. What Amex cards would you recommend?
I think the first to consider is how you use your Amex; ie are you a hilton, SPG or DL loyalist? This will affect whether their co-brand is important to have.
Like an idiot I cancelled my SPG card and regret it now, realizing I prefer SPG to Marriott properties (usually).
The current Hilton offer is for points not nights so that has been considered to be a downgraded initial offer but still useful if you're a regular customer.
If you're a Delta flyer, then depending on how rich your blood is, the Skymiles has now 4 cards-Blue, Gold, Platinum and Reserve. I actually have both the Platinum Skymiles as well as the Reserve...in a year or so will have to decide which is more useful to me. This year I've already booked my companion ticket with my Skymiles Plat award and waiting for my renewal with the Reserve to book another companion trip (this can be done for first class as well as economy). Neither are great for redemptions-1X skymiles for everything except Delta (and I use my Amex Platinum for that) but the MQM earning as well as initial skymiles offered when I first obtained them were helpful. Again, if you're not shackled to Delta I wouldn't recommend either.
If you value Membership Rewards then the Everyday or Everyday Preferred is pretty good; although I see you have the BCP which is a lot like EDP except obviously you earn cash back with BCP not MR. Honestly if we bought a lot of groceries I'd probably have the BCP and use my $6K on that then move on to ED or EDP (depending on whether the fee and the "game" of using it 20 v. 30 times a month is worth it to you).
I love love love my Amex Platinum card-large annual fee BUT I enjoy the small perks with being automatically gold with Marriott and SPG; entrance to SkyClub; the $200 credit with my chosen airline (yep, DL of course but there are others!); 5X flights. It's also nice and heavy (I know, roll eyes) and feels substantial. There are other benefits such as concierge, etc that I don't take advantage of (but should). Membership Rewards transfer to several airlines as well as some hotels but THERE IS A SURCHARGE for US carriers which I didn't know until I started converting MR to Skymiles (I believe it's $0.006/mr point with a max of $99-Amex passes along the excise fee IF it's a domestic carrier).
Amex has business cards under similar branding and TPG and others have blogged about the Business Gold Rewards card which he likes, as well as doubling the initial bonuses and earned MQMs if you have both a business and personal skymiles/SPG branded cards. Unfortunately, I can't speak to business cards but I'm sure there are some who can.
Finally, American Express usually has some decent "offers" and I have saved so far this year almost $500 a year plus earned an extra 14,000 MR (so depending on how much you value those...) and while often the same offers are shown, sometimes only 1 is on a specific card so having more than one Amex can increase the odds of having a targeted (read:good) offer.
In a perfect wallet, I would have the Amex Platinum, the Amex Platinum Skymiles, EDP, BCP and SPG for reasons above. The current thought is Amex limits most customers to 4 charge (like amex plat; gold card reserve, green card, etc) and 4 credit cards, although there are data points with some exceptions. I also go to Doctor of Credit's spreadsheet to gage whether the current offer is the historical highest before getting a card since there's the once a lifetime (usually) language.