Supposedly FICO scoring does tend to see 3 cards reporting as a sweet spot for scoring purposes.. That said... In your situation.. it be good to have a Visa/MC in addition to your other cards.. because theres still a lot of places that dont take Amex or Discover.... You can find something with good point/cashback potential.. may not be "optimum".. And from personal experience, there are good reasons to use an Amex even though you dont get the most points or cashback on the purchase possible,but there still are features like purchase protection and such that can make it more valuable than the points.. As I recently discovered when I dumped a hot tea into my Chromebook..... Fortunately someone on here asked me the question what did I use.. and i was like Amex Cash Magnet... it had a sub and a 0% offer as well as a interesting split payment option... It saved my bacon..... losing 0.5% CB vs the entire purchase cost..... Thats value =)
3 is good for 2/3 of the bureaus, need to be at 4 for EQ FICO 8 though it's an absurdly minor ding.
Sadly the older models you need more, possibly 5-6 and that doesn't include optimization for those of us that have installment loans... need an absurd number of open revolvers to optimize that fully so end of the day I'd probably just suggest 4 revolvers for everyone as even the best FICO 2 optimization for me was only worth +7 points on a clean scorecard.
I'd grab a Citi DC or maybe a US bank cash back card but I would have at least one MC/Visa.... And by at least one I mean 3 or 4 :-)