If you slap something commensurate to the big dish then you might not need to go as high. But yeah. Even still, J75 upgrades could probably squeeze some better performance out of it.
The thing is, a tubojet is so much better at high altitudes than a fan.
 
For those speeds I think you'd have to rework the cockpit, wing leading edges, and other areas, otherwise you'd probably run into thermal issues.

(Somewhere around the internet are various anecdotal accounts of F-111 drivers claiming to hit speeds close to Mach 3 at high altitude, and my recollection was that thermal damage to the cockpit was a big concern. Assuming the claims are true, of course.)
Speed at Mach 2.5 and above becomes an issue. I read somewhere about the F-111 having a 5 min countdown timer for time Mach 2 or 2.5 (don't recall which it was). Read somewhere that the Mirage F-1E would have titanium mods like you suggested, and been capable of Mach 2.5
 

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