Some exchanges like Bithumb have levels of memberships that lets you transact with bigger amounts. I'm pretty sure popular exchanges all have this. You just need to pass some sort of KYC verification. Yes you can also do OTC purchase for an unlimited amount, you just need to find the right party to transact with.
OTC is a tricky proposition. I suggest you do your due diligence and research the pros and cons of OTC.
Are there easy ways to buy bitcoin without hassle?
I recently came across an article that's perfect for that
https://coinadvisors.co/2018/05/27/the-top-10-easiest-ways-to-buy-bitcoin-with-a-credit-card/