I ran Vittoria Voyager Hypers on my Volpe. They were 700x35mm tires, but the measured out at 37mm. They fit fine, though close at the chainstays. I now run Panaracer Gravelking Slicks on a few bikes in 700x38. They measure out 37-38mm. While the Hypers are no longer available
the GKs are and I know they fit on a 2006 Volpe. You might get 40s on there..if you did, it would be closest at the chainstays..narrowest point. Of course..it depends on how the 40mm tire measures out when mounted.
Doug..maybe you can measure the distance between the chainstays at about the point where your 32s or 35s sit..