Narrow building window and subordinate building component

We have a large plot (1000sqm) with a mini building window (6.50x10m). The long side (10m N/S) borders neighboring plots, the width side (6.50m E/W) borders another new building. We share a garage space in the middle. We want the house a bit bigger - it feels very much like a matchbox. N/S is maxed out due to the distance regulation to the neighbor. West is as well, but on the east side we have a lot of space, about 50m space/garden. The limitation is set by the given building window. We were told by the architect that a 1x5m subordinate structure (bay window) is possible on the east side. That is the maximum allowed extension. I have found similar numbers (1.50x5m) in the calculation of the distance area ("...In the calculation of the distance area, exceptions are made (...) for bay windows if they are no wider than 5m and do not protrude more than 1.5m). However, our concern is not the distance area but the building window. So far, I cannot find any information for this constellation. We are trying to get an appointment at the building authority but want to be prepared.

A picture of the development plan and possibly the written provisions would not be bad.

We were told by the architect that a 1x5m subordinate structure (bay window) on the east side is possible.

Where did he get this information? Has he already planned several projects in this development area? Is he very familiar with the practices of the responsible approval authority?
Since you want to deviate from the provisions of the development plan, the nationwide planning law applies here, §31 Building Code:
§ 31 Exceptions and Exemptions
(1) Exceptions to the provisions of the development plan may be permitted if they are expressly provided for in the development plan in terms of type and extent.
(2) Exemptions from the provisions of the development plan can be granted if the basic principles of the planning are not affected and
1. reasons of the common good, including the need to accommodate refugees or asylum seekers, require the exemption, or
2. the deviation is justifiable from an urban planning perspective, or
3. the implementation of the development plan would lead to an obviously unintended hardship
and if the deviation is also compatible with public interests, taking into account neighboring interests.

As you describe the situation, perhaps argument 3 could be used. However, as mentioned above, the details of the property and the development plan would need to be known.