It wanted to start with printing some illustrations, but my printer is kind of bad, and so the intersected thin lines in some illustrations would appear as blob.
This can be solved with a brush where there is a white outline, so no line is truly intersected.
How can I do this, without drawing white lines on the intersection or raising the intersections a bit?
Is there any solid brush with a white outline, if not is it possible to do one?
What Adobe software are you using? You've inadvertently posted in the non-support, non-specific Forum Lounge. Let us know what you're using and a moderator can move your post to a software-specific, support forum.
This is not possible to do. However the good news is that you don't need it to be able to be done.
You should be able to just use whatever brush/tool you normally use. Convert it to a path and add a white stroke to it.
If that doesn't work, could you provide some screenshots of what you are trying to do?