Managing director in more than two companies

No.

A company may appoint or employ a person as its managing director, if he is the managing director or manager of one, and of not more than one, other company- Provisio to Section 203 (3) of the Companies act 2013

is clause 203(3) applicable to private companies as section 203(1) is not? are the two sub sections independent of each other?

Appointment of KMP is not mandatory for private company. However, if pvt company is appointing KMP, they have to comply with the regulations.

great thanks!!