Planning extension (foundation/load-bearing capacity/alternatives)

4 x 57m2 new construction + costs for unknown demolition, reinforcement, and other renovation works on the existing building will rather and at least including incidental construction costs gross be between € 500,000 - € 600,000. Without knowledge of the specific construction task and the structural context, such calculations remain pure speculation.

Alternatively, it would make sense to ask another structural engineer.
In existing buildings, this is quite common until the right one is found.
We do a lot of planning in the Rhine-Main area, and there rooftop extensions are often the only solution.
A steel skeleton can be located inside or outside the existing building envelope. Today, it is often also desired that all interior walls in an existing building be removed.
The existing foundations may possibly be completely excluded.

There is nothing dreamy about that; how else would you realize residential units on a hall roof, even timber construction has its weight.
It is hardly going to be a social housing project.

In addition, the upper building closure must already comply with the Energy Saving Ordinance since 2015.

The existing foundations may possibly be completely disregarded.

The steel frame ones would have to be quite close by.

There will hardly be any social housing planned.

Which premium tenants do you think are eager to move into 57 sqm in the Voreifel?

Well, Euskirchen is quite sought-after and had one of the highest or the highest rent increases in 2018. Additionally, it is close to the city center with train and highway connections to Cologne+[Bonn].

Well, Euskirchen is definitely very sought after

Sought after? Well, then the rents would be higher. On average, you're paying around €7.50 there, and more than €8.50 for a complete new build does not exist.
Then try to make your investment look good.
4x57 sqm at €8 rent is €22k per year.
Let's roughly calculate €2k construction costs for the extension, then rounded up, we come to a slim €500k (including additional construction costs). That is a gross yield of 4.4% BEFORE management and taxes. Total nonsense. To get by decently, it should be 6%. That would shrink your budget to about €370k, which would then be €1,622 per sqm of living space for a technically demanding solution. And that, in turn, will not work.

If the rest of the house and the location are not also as good as a new build, it won't work with the top rent either and your investment will drift further and further away...

By now I get €500 cold rent with every new lease and people really line up. Maybe I should be thirty percent higher? The house was built in 1957, partially insulated 15 years ago, and a central heating system was installed. If there are no curtains in the window, strangers ring the tenants and ask if the apartment is available. For new buildings and first-time occupancy, I even expect €9 or more per square meter. I actually don't find it cheap either, but apartments of this size are almost nowhere to be found on the market. One almost tends to build 5 x 45 sqm instead, because then even more people queue up. But the economic calculation is my problem. However, since I urgently need a new roof, a roof without added value would probably be an even worse investment or am I making a mistake? And by roof I really mean everything, not just tiles and insulation.