A healthcare professional may obviously extend his or her stay for personal reasons but all additional costs linked to this prolongation are at the charge of the individual. To learn about the impact on the flight, see FAQ 12.2-3.
If the extension is for professional reasons, supporting documentation must be included with the visa application (for example, a scientific program or an email confirming that the professional must remain or extend his stay for professional reasons).
Yes, with the proviso 1) that transport costs are not higher than they would have been if the healthcare professional had not extended his or her stay (if this is the case, then the healthcare professional must pay the difference in price himself) and 2) that the duration of the extended stay remains accessory in relation to the duration of the scientific event.
The following table indicates when an extension of a stay is considered as to be accessory:

* By ‘extension’ it is understood all the days without scientific activity.
The company must limit its contribution as being towards transport costs linked directly to the scientific event. In concrete terms, the part paid by the company is limited to the fraction of the total cost obtained through multiplying the total travel costs by a fraction of which the numerator corresponds to the official duration of the scientific event in (half)days, and the denominator corresponds to the total duration of the stay, also counted in (half)days.
For example: a doctor participates in a scientific event in Rome for three days and then extends his stay by three days in order to visit the city – a total of 6 days. The company may only fund 3/6ths or half of this healthcare professional’s travel expenses, the other half being at the doctor’s expense.
Important: In the case of a non-accessory extension of stay, it is not sufficient to cover only the outbound or return trip, unless the cost of that trip does not exceed the professional portion of the flight. This must be demonstrated by clearly indicating the total duration of the stay (including the extension for personal reasons) as well as the total price of the outbound and return trip in the visa application so that the aforementioned proportion can be calculated accurately. Only in this way can the professional portion of the flight be calculated relative to the private portion