>>1903069Budapest has this suburban rail system called HÉV (picrel), that end isolated without a trunk line.
In the suburbs, they often can't be reasonably grade separated, so the connecting tunnels would need to have overhead wires. It's less S-bahn, which is in black, and more of those fake U-bahns many German cities like Frankfurt and Stuttgart have (There are only 4 proper metro systems in Germany)
The north-south tunnel is a standard plan to connect 3 HÉV lines. The trouble is the Gödöllő HÉV on the right, its terminus facing off against the terminus of Metro line 2. To connect it, we would need to retrofit the entire M2 tunnels for overhead wires.
Honestly, I'm not sure how expensive that would be, or could M2 maintain its frequency. If it's not worth it, we would have to settle for building a more comfortable transfer.
But if it's possible, it would still not cover all of M2's capacity, so some of it could branch out as a metro service. And on the Buda side, suburban rails could be integrated with the tram line to Hűvösvölgy (pretty fast line as far as tram lines go, could have been a HÉV line if history goes differently.) and later possibly a tunnel to Budakeszi.