A titanium system that is already fitted can be shortened, extended, re-hung and re-tipped. What it will not tolerate is being treated like stainless. The material moves heat differently, it reacts with the atmosphere sooner than steel does, and it work-hardens quickly at a cut edge.
None of that rules out modification. It sets the terms. Anyone who has welded titanium on a bench will recognise the same requirements on the car, with less room to meet them and a good deal less comfort while meeting them.
Titanium wants a clean, oxygen-free environment around the weld, and it stays sensitive to the atmosphere for longer after the arc has stopped than stainless does. On a bench that means a trailing shield and a purge. Under a car it means the same, plus the difficulty of sealing a run that is open at both ends.
Heat also spreads into everything titanium is attached to. Rubber hangers, heat shields and any wiring near the run are closer to the weld than they would ever be on a bench, and none of them benefit from the temperature a titanium seam needs.
Cut titanium with a method that does not drag contamination into the edge: a fine abrasive disc run at moderate speed, or a saw with a blade kept for titanium. Anything that has previously cut steel should be cleaned before it touches this material.
The cut edge work-hardens, so dress it lightly and do not over-file. A heavily worked edge becomes difficult to fuse and encourages the kind of porosity that shows as a rough grey seam once the part is back on the car and hot.
A purge on a fitted system is a compromise, and it needs to be a deliberate one. Seal the far end, feed gas into the near end, and give it long enough that the gas has actually reached the joint rather than merely passed the regulator.
Where the run cannot be sealed, a local dam either side of the joint will do the job, provided it is removed afterwards. A dam left inside a titanium system is a rattle waiting to happen, and the owner will blame the exhaust rather than the repair.
Titanium records its own heat history in colour, and that record is worth reading. A pale straw or light blue seam says the shielding held. A dull grey or chalky white surface says the metal was exposed while it was hot, and the joint will be brittle there even if it looks tidy.
That is why a modified titanium system should be inspected after the first heat cycle rather than only at the moment of welding. The colours settle, and a seam that looked acceptable under workshop light can look very different once the part has run hot on the road.
Sections already welded several times, thin wall tube near a bend, and anything showing a chalky surface from an earlier repair are best replaced rather than reworked. Each additional heat cycle takes something out of the material, and titanium does not give it back.
Where replacement is the answer, matching the original is easier than it looks. A titanium exhaust system built from consistent tube will accept a new section cleanly, and the parts used to make the joint, from TIG titanium welding parts to the filler, should be titanium throughout rather than whatever was in the drawer.