If you're willing to provide ID verification and you live in a country that they deal with, you could try
Coinbase (there will still be limits, just higher ones).
If you're not willing to provide ID verification, you most likely won't find anywhere to deal with larger amounts. On LocalBitcoins most traders dealing with it will ask for ID since it's a risky payment system (with chargeback fraud being very common).
Wherever you find, you'll end up with high fees, because using a credit card is a pain for pretty much everyone involved.
