Combine Business and Economy flights [duplicate]

I have the weird habit of really enjoying Business class flights while not wanting to spend all of my money on flight tickets.

As of now, I have always been using Google Flights or ITA Matrix to search for Business class connections from my hometown to an airport close to my destination, and then book a cheap economy carrier to my destination, or book a cheap economy carrier to a close country in Europe and then take a business class flight to my destination.

For example:

Case 1:

ZRH (Zürich, Switzerland) -> PTY (Panama City, Panama) in Business.

PTY -> BOG (Bogota, Colombia) in Economy.

Case 2:

ZRH (Zürich, Switzerland) -> PRG (Prague, Czech Republic) in Economy.

PRG -> HND (Tokyo, Japan) in Business.

Is there any search engine that lets you search for this kind of combinations without entering manually all the stopover possibilities?

EDIT:

I don't think it's a duplicate, because the linked question is asking for flight options in premium economy when possible, economy when not. I am specifically asking for the possibility to define business for the longer leg, and eco for the shorter, whilst not having to search every stopover destination by hand.

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Can you link two separate flights with the same airline?

A: It depends, but the general rule is NO. Some airlines will through check baggage onto separately ticketed flights, but some won't (even if both tickets are with the same airline). Some airlines will take pity if your delay is due to them, but others don't.

Can you combine flights?

It's possible to buy flights from two different airlines when booking, just add each flight one at a time. i.e create a trip with two one-way flights instead of a return trip. Good to know: Two one-way flights with low-cost airlines usually come to the same price as a return flight with one of them.

Can you book overlapping flights?

"Nested ticketing" or "nesting itineraries," sometimes also called "back-to-back flights," could help you save a ton on flights, but may be a little risky. It works best if you need to book two trips to and from the same destinations (say, going home to visit your family for Thanksgiving and then again for Christmas).

Is flying business class the same as first class?

First-class passengers might have a seat that turns into a bed or even their own private apartment. Business-class might offer more legroom but doesn't offer a private space. The food and drink in business class are typically at a restaurant level.

The Economics of Airline Class

Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.

Images: David McBee, John Guccione www.advergroup.com, David McBee, Pixabay