Add an apartment and divide the land

However, §34 of the Building Code could cause problems here, since it would no longer be a detached building, but a terraced house.

More likely a semi-detached house, since the OP refers to boundary distance regarding the neighbor.

I own a 1200m2 plot, built with a two-family house, freshly renovated. As can be seen on my very simple drawing, I would have space next to my house for an extension of about 9mx9m (I have assumed about 4 meters boundary distance here).

Thank you very much for the answers so far, unfortunately I have been away the last few days, so no feedback from me.

If we were to build bigger after all, for which we would need another loan, does anyone know how the bank would behave? Can such a real estate loan be "easily" increased at the agreed conditions? It would be worthwhile for the bank, as there would be more interest income and, due to my 130k equity, an overall lower loan-to-value ratio for the entire property. I estimate the additional rental income at about €1400, minus tax.
We financed the house with the DSL Bank, of which about €390k remaining debt will be left at the end of the year.
I would estimate the costs of the complete extension at about €350-380k, so we would still need about €250k.

Income-wise it would look like this:
Monthly income €4700 (our loan currently costs €1230) + assumed €1000 rental income after tax (Is that about right?) = €5700 per month.
The new loan would be about €1960 per month at current conditions. We would thus have just under €300 more to live on per month.

I shouldn’t even think about my debts then... but there would also be a value behind it...

: Yes, it would basically be a semi-detached house