<p>When printing several objects, I recently encountered a problem that arises when the structure in itself is relatively thin or the support towers have a small surface: the printhead would in motion tend to knock one or more over as it traveled or catch at them and create layer shift.</p>

<p>How can I avoid collisions with the already printed parts of a layer?</p>

The problem was twofold:
Lack of bed adhesion due to the small contact surface
motion into the already printed objects.
The
quick and dirty
way was to change two settings:
Print with a small (3 mm) brim to stick the supports to the print and provide more surface. Other materials than PLA may need considerably more brim!
Activate Z-Hop to force the nozzle to lift over the print when traveling
These tricks don't solve issues with very thin structures or in all cases. In those cases, it can be mandatory to increase the structure's (support) thickness or change the alignment.