Here is the summary I received from my Serbian partner - reputable banking lawyer:
Main problem with non-resident companies and accounts in Serbian banks is that foreign company need Serbian tax number in order to open accounts.
It’s relatively easy to obtain it. This tax number is main connection to Central bank and there are reports which have to be filed by the bank.
Even if you find bank who accept the non-resident client without such number, it’s because they have no previous experience.
After two months, when Central bank start to require information and documents, they will either propose astronomical charge or they will close the accounts if you don't have this number.
And with this number you need to fill up documentation every month - if you don't do it, your account will be blocked.
Another thing:
Please note: In Serbia there is a relatively new tax rule.
We have 52 jurisdictions which are considered as off-shore tax heavens.
If you make a payment to this 52 countries for services, the company will be liable for 20-25% tax on the amount remitted abroad. In order not to be liable for this tax, counterparty must provide Tax Resident
Certificate which will prove that company’s management is actually doing business from this country.