You can re-sleeve the one that's already been sleeved.
It's .040" already? Have you had it sonic checked? Most 340's will take a .060" overbore without any problems. The '68 340 in my duster is .060" over. Of course it might not clean up with only another .020" cut, don't know what you're working with or what it will need. There are guys out there that do .080" bores on 318's, just depends on the wall thickness. But if you go more than .060" you'll probably need custom pistons, so, more cost there too.
Usually it's $50 a sleeve, though it can be more. That's an extra $400 for machine work on top of the normal costs. If it's not number matching deal Id be looking for a 360.