Upvote:2
Most of the time, this cannot happen. You might be able to contact the airline/airport in advance and they might do this for you, but I doubt it.
The only other reason is if both of the airlines are members of the same group, e.g. Oneworld, then they could have this done for you.
Upvote:3
The process of having multiple airlines handle your bags is called "interlining". In order for that to happen the airlines MUST have an interlining agreement in place. This agreement manages cost,tracking, liability, data exchange, etc. of the baggage transfer.
All airlines that are in the same alliance do have interlining agreement, but interlining typically extends a significantly past the alliance. However, the information is not easy to find.
If there is not interline agreement, there is no baggage transfer.
If there is an interline agreement, it's possible that a baggage transfer could happen, but this depends a lot on how the ticket is being booked.
Can a private humble human being achieve that?
Not unless you book it as a single ticket. Your best shot is to call a knowledgeable travel agent, they have access to data & information that you don't, plus a (hopefully) lot of experience. This will cost you extra, so you need to decide what it's worth to you.