I'm a graduate student in the US since Fall 2013. While I started working at my university the same year, I applied for my first credit card(Discover it) only during March 2014. After about 6 months(Oct/Nov 2014), I wanted to apply for another one, but as my credit history was only a few months long then, I settled for a credit card of the bank(PNC) where I had a checking account. Both these credit cards were approved after a review period(3-5 business days). After this, I had no intention of applying for more credit cards.
This year during May, I received a pre-approved offer for the Chase Freedom credit card. My credit score was about 740 at the time, with about a year and a couple of months worth of credit history. I found mostly very good reviews of this credit card, and so applied for it immediately, with $2.5k of credit line.
Within another month, towards the end of June, I got a pre-approved offer for the American Express Everyday credit card. Again, I applied for it and was approved immediately with the same credit line as Chase Freedom's.
My credit score as of now is 703 (I assume due to the multiple lines of new credit), and a couple of days back I received an offer for the pre-approved Capital One Quicksilver credit card. There are some appealing points in this card, such as unlimited 1.5% cash back, and access to higher credit line after 5 monthly on-time payments. The offer is valid till sometime in September.
Nevertheless, should I stay away from a new credit card at the moment? I feel four credit cards are sufficient as of now, but again, more credit equals to lesser utilization which helps build up the credit history (and score) over time, or so I heard. Should I look for another credit card somewhere around mid-2016 next instead?
I have no loans, and I have made all my monthly bills in full every month so far. The credit limit for the other two cards(Discover and PNC) is $1000 each. My total credit history length so far would be about one and half years.