Multiple countries is the primary reason that corporate income tax doesn't work. International corporations just report profits in the countries with the lowest taxes. Corporate profit doesn't have any physical existence, it's just numbers in a spreadsheet, you can trivially move it to any country you like.

The only way to tax an international entity is to tax them on the things that actually exist in your country: Customers, employees, property, etc. But that's not corporate income tax anymore, it's sales tax, personal income tax, property tax, etc. The closest thing you can get to corporate income tax that actually works is VAT.