I want to know if only travel agents can book connecting flights of different airlines on a single ticket or is it something anyone can do. If so how?

Say there are two flights A and B operated by airlines A1 and B1.

Can I simply call Airline A1 and book ticket and then call B1 and book another ticket and ask them to "append it to the same ticket" as that of A1?

edit. For example: A1 is China Airlines from TPE to BKK, B1 is Jet airways from BKK to BOM.