Is there a tool for planning "nested" round trips?

Question

We want to go to Japan. We've checked some flights, and reached an interesting conclusion. First, a normal round trip:

• A round trip from Tel Aviv to Tokyo, Sep-26 - Nov-5, costs $880. There are very few "cheap" flights - the fifth option is already at $1146.

But then:

• A round trip from Madrid to Tokyo, Sep-26 - Nov-5 (same dates) is as low as $620, with many similar options under $800.
• A round trip from Tel Aviv to Madrid, Sep-23 - Nov-8 costs about $300, and there is even a non-convenient flight for $200! (9 hour overnight layover)

So, if I take the cheapest options, I can fly directly to Tokyo for $880, or combine a trip to Madrid and Tokyo for $820 - this is both cheaper and more fun.
Even if I take a "better" flight to Spain it might reach $920 for the combined trip - still well worth it (extra $40).

I've looked and found a similar concept called hacker fare, and also this related question: Is there a flight search engine that combines flights from different airlines?
In my case, unlike hacker-fare, I want two round-trips, and I don't particularly care where the "layover" is - it could be any nice city.

Is there a tool that can help me plan such a trip?
For example, showing the two round trips, or showing bulk data to/from popular destinations?

Answer 1

Matrix is your best bet for this type of stuff, and it will still be a sub-optimal two-step optimization:

1. First I'd try to find the intercontinental leg of your flight, i.e. the one that brings you to Tokyo, and we are basically free to start from anywhere. I once asked a similar question
   Flight Search from anywhere to a specific destination
   but for caveats explained below, I suggest another trick: In Matrix pick an airport that is central, i.e. if you were looking to have your stop-over in Europe use FRA and select the Nearby option, choose maximum radius and hit Select all.
   This gives you a list of cheap intermediate destinations.

2. In a second step you can now (manually) filter those for how much you would like to spend time there and for how cheap it is to get there, using the search tool of your choice.

I'm afraid this does not answer your question in the sense of is there a tool? but it is the best solution to your problem. If you are asking me explicitly for the tool, two sites I presented in a different answer, azair and kiwi, would be good tools, but they fail for intercontinental travel and looking this far ahead.