The fact that the two airports are not served by a single common airline does not mean you cannot book flights from one to the other from one of those airlines.
Most airlines have various forms of partnerships (interlining agreements, code shares, alliances...) which allow them to sell itineraries which include flights from many other airlines.
It does not necessarily mean that you can get any combination of flights/airlines, but it increases the possibilities quite a lot. The most notable exceptions are low-cost carriers, who very often don't even sell connections between their own flights, much less to/from other airlines.
You can start by looking for flights on Google Flights or any other flight search engine, they will tell you possible combinations.
For instance getting from Paramaribo in Suriname to Ko Samui in Thailand can be done like this:
As you can see, it involves 3 flights from 2 different airlines (and takes quite a while), but it's a single ticket.
Note that some engines will only show such combinations, while others (like Google Flights, Kiwi, and a few others) will show both these AND those involving a self-transfer, but will usually flag them as such. See below about that.
If you book via a third party, two situations may arise:
- The itinerary can be bought as a single ticket directly from one of the airlines.
- The itinerary cannot be bought as a single ticket, and they just go ahead and buy separate tickets for you, possibly including some vague promise that they will help you if this go awry, which often turns out to not quite work out.
In neither case does the OTA actually bring much value (other than possibly highlighting the existence of a combination).
So book directly with the airline(s). Note that sometimes, you cannot book the itinerary online directly with either airline, you will need to call them. The OTA may bring additional flexibility at this stage (letting you book online directly), but the drawbacks later on if issues arise and they start playing ping-pong are real. It's already complex enough with 2 or more airlines involved, it's a nightmare when you add an unmotivated OTA on top. It's up to you to determine which is more important to you.
If they are able to sell the whole itinerary on a single ticket, you are protected: if you miss the connection, or if they change the schedule or cancel either flight, they have to make it right (though the procedures and protections may vary depending on the countries involved).
If it's not possible to book the whole itinerary as a single ticket, and you book them separately (a so-called "self-transfer"), remember that there are lots of possible additional issues:
- If you miss a connection, you are on your own (onward ticket may be cancelled, including subsequent flights on the same ticket, like a return flight, and you need to find and pay for a new flight out of your own pocket
- If they change the schedules or cancel a flight and the new schedules no longer work together (first flight arriving after the second flight leaves...), you are on your own
- You may need more visas if you transit in a country which requires one
- Baggage allowances may not align
- Even if everything goes well, you need more time for the connection, especially if you have hold luggage, as you need to wait for your bags, and you need to check-in for the next flight before the check-in deadline (often around one hour before scheduled departure)
- You may have to spend time going through passport control and/or security which may not be needed in other circumstances
Self-transfers are best for seasoned travellers, and require careful consideration of the risks involved (Can you book a new flight timely and cheaply, even at the last minute, if you miss the original one? Can you afford the extra costs?). Having several hours between the flights is strongly recommended, ideally even an overnight stay.
Note that even when the whole itinerary is booked as a single ticket, you may want to stop in intermediate cities (because you want to break up a very long trip, or because you want to visit said city). This is still possible with the "multi-city" option available on most booking engines. Note that depending on the policies of the airlines involved, it may cost more than a direct connection.
To take your initial example, I see the following cases:
- I want to get from SRC to DST and I don't care about MID, and I can book the SRC-MID-DST directly from the airline as one ticket -> buy that
- I want to get from SRC to DST and I would like to stop in MID for a few days (in both directions): I'll check the options of buying SRC-MID-DST with stopovers and SRC-MID + MID-DST (both directly from the airline(s)) and buy the cheapest
- I want to get from SRC to DST and I don't care about MID, but I can't book the SRC-MID-DST directly from the airline as one ticket -> I'll first look for other alternatives. If none are convenient, I'll buy SRC-MID and MID-DST separately, directly from the airline(s), but I'll have a lot of buffer in between (how much depends on the exact flights, including their frequency, duration and cost).
Remember: very long delays are relatively rare, but they DO happen.
Also don't forget to take travel insurance, and read the fine print to know what they covert or don't cover, in what circumstances.
