its not a hard encoded rule like 5/24, but getting 5 chase cards within a year, ive seen people get shut down for. Actually, spending money is what makes chase nervous because they think you apply for a load of credit in a short period of time, use your cards, then stop paying them all. they call it a bustout. I think they are slowly denying app for that now... someone recently here got the too many inquiries in a short period of time.
the rule suggested for chase shutdown is to try to stay below 5/12, 3/6, 2/3.
I think your moving too fast with Chase.
@SouthFayetteFan may have a different opinion though. haha. tagged him for his response.