Can a star emit a larger fraction of its total light in the visual range than the Sun does If one sets both the bolometric and visual luminosity of the Sun to 1 (and use a linear scale), can a star then have a higher visual than bolometric luminosity?

It makes sense that this will not be the case for most stars, as smaller stars will tend to radiate more of their energy as infrared, while larger go more into the ultraviolet. That is, this is inherently linked to what wavelengths the human eye has evolved sensitivity for. But are there exceptions? If there are, I would think they have parameters very close to the sun.
Surely this is exactly what the V-band bolometric correction assesses. The numerically larger the bolometric correction, the more of a star's flux (as a fraction) is in the V-band.

The Sun's bolometric correction is about -0.06 to -0.11 mag, depending on which sources you look at. Cool stars and hot stars have numerically smaller BCs and emit a bigger fraction of their flux outside the V band.

Some sources put the BCs of A5-G0 stars as very slightly larger than the Sun's, by up to 0.1 mag (e.g. Pecaut &amp; Mamajek 2013).