Is it possible for a fellow to work 6 months per year as an MSCA fellow and the other 6 months in an academic position at another institution in another country if they get an approval by the PF host organisation and the other institution?

They would need to discuss this with the project officer, and they can approve or refuse the request. Part time working has to be calculated on a weekly basis as the payments are based per person month. For 6 months on, 6 months off, they would need to suspend the project for the 6 months they are not working on the MSCA fellowship.