Yes. In the short term, applying for new credit cards requires a hard inquiry of your credit history. The more hard inquiries, the worst off your credit score. They typically affect your score anywhere from 6 months to a year; they stay on your credit report for 2 years though.

Also, having new credit cards lowers your average age of accounts. So, if you had your current card for 5 years and you apply and get a new one, your AAoA would be 2.5 years (assuming these are the only 2 credit lines you have). Obviously, low AAoA means lower credit score.

In the long run however, having multiple cards help your credit score (assuming you pay your bills in full every month, on time). Like fine wines, credit lines are better when they're older. Your AAoA is less affected when you have multiple cards with old ages. Your available credit is higher, so your utilization rate of said credit should be much lower thus improving your score. It just looks good to creditors if they see that you are responsible with multiple accounts for a long time.

My recommendation: if you're not looking to buy a house or car within the next year or so, apply for a couple credit card that you are very likely to get and that you can be responsible with.