The best way to manage this kind of process is to put the employee in one payroll country only, then this country will make charges to the other countries that are using the services of the Expat or Inpat.
So, you must be sure to complain with all regulation, taxes, etc. that are caused in the country base, and the other are managed throught interco charges.
If you think, you need more help. Do not hesitate to contact me.
Carlos Javier Medina