Is there some functionality to draw curves ontop of objects that is similar to topobuild but does curves instead ?

Template the upstream node.
Add Curve SOP in current network or in another object.
Turn on Multi-Snap
Open Multi-Snap Options and turn on template snapping.

Now you can draw curves on surfaces.

I also like to shade my template geometry as hidden line ghost. Display options for Template Geometry.

Thanks! I came to the conclusion of a similar approach just different shading but here is a follow up question, is there a way to make several curves with one curve sop or do I have to add a new Curve SOP for every curve ?

You know you have a point.

The Curve SOP is limited to a single curve per SOP.

But…

The Stroke SOP lets you stroke out as many curves as you want.

Please submit an RFE for the Curve SOP to have the same multi-curve functionality has the Stroke SOP.;

Submitted, and thanks for the answers !