Enlarge living room / extend concrete ceiling?

Yes, the garage is located directly on the boundary. According to a brief inquiry from the town hall, a boundary distance of 2.50m must be maintained. Since the garage is about 3.4m wide, I would have less than one meter of clearance in this direction.

In your plan, it is more like double that. So if you extend by 90 cm over 6 m depth (assumed), that would be about 5 m2 gained. Then prices per extra m2 could be like in Central Manhattan.

Cheaper would probably be the 1/3 rule applied in many federal states (which one are we even talking about?): You can move up to 1/3 of the house length closer to the boundary (often up to 1.5m) if it is a stairwell or a bay window.

So for a fictitious 9 m house length, on 3 m length a lintel, remove existing wall and move about (3.4-1.5)=1.9 m depth towards the neighbor. At least nearly 6 m2. You can also equip the bay window with (frosted) glass.

What valuable rooms are located in the basement on the relevant side? If in doubt, I would simply close the windows or, since it is a slope, raise the additional area so that the windows remain. So light: rather no, air: yes.

Although I also wonder whether I am allowed to undercut the boundary distance with the neighbor’s permission

If they still have more than 2.5 m of space to the boundary, yes. This is called building encumbrance (Baulast). Does the neighbor still have 20 meters of space to your boundary? If not, this reduces the value of their property and possibly prevents a later extension on their part. As a neighbor, I would make that very expensive if at all. Very expensive!

And regarding the extension towards the upper part of the plan, I would first look into the development plan to see if the building line even allows such a thing.

Your plan actually shows about twice as much. So if you expand by 90 cm at a depth of 6 m (assumed), that would be about 5 m2 gained. Then prices per extra m2 would be like in Central Manhattan

Unfortunately, yes.

Cheaper would probably be the 1/3 rule valid in many federal states (which one are we even talking about?): You can also move closer to the boundary on 1/3 of the length of the house (often up to 1.5 m) if it is about a staircase or a bay window.

The plot is in BaWü, city center location. That means €1000+ per sqm. In theory, practically there are no plots left.

So with a hypothetical 9 m house length, a lintel over 3 m length, removing existing wall and moving in depth towards the neighbor by (3.4-1.5)=1.9 m. At least almost 6 m2. You can also equip the bay window with (frosted) glass.

The living room as you now see it on the plan (existing) is about 5x5 m.

What valuable rooms are located in the basement on the respective side? If in doubt, I would just close the windows or, since it is a slope, raise the additional area on stilts so that the windows remain. So light: rather no, air yes.

Standard basement room/hobby room with underfloor heating and carpet.

If it still has more than 2.5 m space to the boundary, yes. It is called building encumbrance. Does the neighbor still have 20 meters of space to your boundary? If not, it reduces the value of his property and possibly prevents a later extension on his part. As a neighbor, I would have that paid for, if at all. Very expensive!
And regarding the extension towards the top of the plan, I would first check the development plan whether the building boundary even allows that.

Thanks, I just checked. Yes, there is a building encumbrance registered on the neighbor. There is no development plan because it is not a new residential area and everything around is basically already built up.

Apart from the fact that I do not want to give you any hopes here - at least for a somewhat economical - solution: at least the (preferably not only partial) floor plans of all three affected floors (i.e. also of the deducting and the superimposing ones) should be made known to the discussants, otherwise one might as well roll the dice or ask Deep Thought (42).

Apart from the fact that I don’t want to give you any hopes here — at least for a somewhat economical — solution

There is no economical solution. The money invested in the expansion will never come back. This is a luxury project. If you accept it as such, it doesn’t hurt as much anymore. Plan your ideal living room with an architect, then check the price. If it works, it works. If not, then consider with the architect how you can get closest to the ideal solution within the given budget.

I see it the same way as The project is out of proportion. I also find the scale of the planned extension a bit quirky - it's no longer an extension: it's a possible expansion in every direction. One should really come down from the dream cloud. Otherwise, one would have already known before the purchase that the space is too small. How many sqm is the living room? It looks quite okay... is the room for dining and living? Can dining be separated? Maybe something is possible elsewhere? Basement windows wouldn't bother me, if necessary you can make windows in the floor of the ground floor, that's original. Otherwise, I would rearrange living spaces differently, e.g. take books out of the living room and set up a reading room elsewhere and yes: the mentioned conservatory can also be a masonry one. I don't see any floor slab problems now.

Apart from the fact that I don't want to raise your hopes here – at least not for a somewhat economical – solution: at least the (preferably not only partial) floor plans of all three affected floors (so also of the one below and the one above) should be made known to the discussants

I'm not interested in an economical solution. The money that goes in there I will never see again anyway. Or maybe a small fraction of it upon a sale. The house still has a first floor, an attic, and a basement. The rooms above and below the living room have exactly the same layout as the living room. I would also like to enlarge the window right away, details further below.

Plan your ideal living room with an architect, then look at the price. If it works, it works. If not, then consider with the architect how you can get closest to the ideal solution with a given budget.

Thanks for the tip. As I said, I would be grateful if someone could give a very rough estimate of what they think something like this costs. Of course, that's not reliable and depends on my preferences.

I also find the dimensions of the planned extension a bit quirky – it's not really an extension anymore: it is a potential expansion in every direction. One should come down from the dream cloud. Otherwise, one would have known before the purchase that the room is too small.

Whatever the difference between an expansion and an extension is.

How many sqm is the living room?

Just measured. About 4.20m x 5.20m, so roughly 22 sqm. In the course of the extension, I would also like to massively enlarge the window. At the moment, it's only a "normal" window. I would like a floor-to-ceiling pane that covers as much of the entire wall as possible in terms of width and height.

It looks quite okay... is the room for dining and living? Can dining be separated? Is something else possible elsewhere?

The dining area is already separated. But that's not the issue.

Basement windows wouldn't matter to me, if necessary you can make windows in the ground floor floor, that's original. Otherwise, I would sort out living spaces differently, e.g., move books out of the living room and set up a reading room somewhere else and yes: the mentioned conservatory can also be a brick one

The basement windows are not that important to me now. But that would be the "cleaner" solution overall. I hope I have answered everything. Thanks, spyfromtheeast.