6 months ago I had 2 live cards:
1 Amex Delta Gold and 1 Mastercard
I now have....hmmmm, let's see:
Amex Delta Skymiles Gold
Amex Membership Rewards Gold
SPG Amex
JetBlue Amex
HHonors Amex
Hilton Citi Visa
Citi AAdvantage Personal Visa
Capital 1 Venture Card
I guess that's 8

Easily the most I've ever had at one time.
6 Months ago my wife had 1 visa card.
She now has:
Amex Delta Skymiles Gold
Amex Membership Rewards Gold
JetBlue Amex
Citi AAdvantage Personal Visa
Citi AAdvantage Business Visa
Capital 1 Venture Card
I applied for all of these on my wife's behalf, lol.
We are now planning ways to use our 700K points/miles.