That's a good question. But just to give you a brief history of myself, I used to collect credit cards. I kind of stopped years ago, but not for the having too many inquries on my credit record, but I was sort of opening myself up to credit fraud having too much information on myself out there. That said, I have over 400 credit cards, and close to 1/2 of those show on my credit report (Trans Union), although most obviously are closed because of inactivity. Most are department store cards, but I do have a couple of dozen open MasterCards and Visas. I asked for a credit report via Trans Union a few months ago. My score on it (similar to the Fair Isaac score) was 931 out of 934. That score alone should dispell the myth that having too many unused credit cards will hurt your credit record. With all those credit cards, I was easily approved for a home loan (Wells Fargo Home Mortgage). I was candid with them with what I did, and they didn't care, since my high credit score said more about me than anything else.
But the reason my score is high is I don't apply for many cards at all right now (too many recent inquiries will hurt your record) plus I always pay my bills on time, with most all my credit cards I pay in full.
But what will hurt your score will be having zillions of cards, and running large balances on them. Large balances might indicate you're getting in over your head, even though you're keeping up on payments. Minimum payments on credit cards could take decades to pay-off, if that's all you do.
So my advice is to keep your credit card balances low, never pay a bill late (allow plenty of time for payment checks you send to arrive in the mail) while maintaining good finances overall. I've heard mentioned if you create a large balance on a credit card and pay it off immediately, will create good credit over time. That's hard to say, although doing that with a single credit card issuer may make them inclined to raise your credit limit, since you've shown you could manage large payments.
Anyway, this is my 2 cents worth.