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If your frame is in the way of a header, would it affect the frame in a bad way if you were to weld a sort of box or diamond as part of the frame. Then running the header through the hole, making sure there is enough clearance for movement. So, the frame in my mind would be stronger since it has been more or less doubled in that spot.

Lots of variables here, are you hacking out a diagonal, or one of the longerons?

In any event if you just replaced a straight piece of material with a "box or diamond" sort of thing you could actually be weakening the structure in torsion by allowing that member to "parallelogram". You need to think this through very carefully.

I concur - it would be better to modify the exhaust if you can...

If you need to remove one of the side diagonals for header clearance, you could replace it with a "V", this should give you the area to run the exhaust thru between the "V" and still keep the side triangulated. Allow at a min 1/2" clearance between the header and any of the frame tubes.
Good luck on the exhaust & frame mods Dave W