Dear Sanjeev,
Every Shops and Establishments Act is a state legislation applicable to those business entities falling within the definitions of 'shop' or 'establishment' as defined under the same and situated within the particular state. In addition, it is basically unit-specific, i.e., each and every unit of the same common business entity, like branches situated in different places within the state, would be treated as a separate establishment for the purposes of the Act. Likewise, the branches of the entity, if situated in different states, would be covered under the particular state's S&E Act only.
It follows, therefore, that you have to take registration under the Delhi S&E Act for the 3 branches in Delhi separately and 15 other branches situated in different states under each state's Act on a branch-wise basis.