Hi,I'm Miranda, and I'll be happy to help you with your question.
There is really no "ideal" amount of credit cards that you should have to build a strong credit score. Many people say to have as many as you need, but no more than you can handle. I would say a safe bet is 4-6 credit cards because you have several different lines available to you. Essentially, you're not putting all of your eggs in one basket.
However, the most important thing is keeping your accounts in good standing. Pay your credit card bills on time and keep the balances as low as possible. Having a bunch of maxed out credit cards can damage your credit score, while having the same amount of cards with $0 balances can help your credit score. However, make sure that you use the credit cards occasionally for small purchases and then pay them off to show an active credit profile with a positive payment history.
If you choose to apply for new credit cards, make sure to do it in moderation because every time you apply a "hard inquiry" will be added to your credit report, and multiple hard inquiries can lower your credit score. Also, having a lot of new credit cards can lower the average age of your credit lines, which can damage your credit score.
I hope that answered your question. If you have further questions, please ask. It's been my pleasure helping you. Please remember to rate my answer positively, as rating me is the only way I receive payment/credit for my work. If you would like to request my help in the future, please post your question with "For Miranda Only" at the beginning, and I will respond.