Of course it's possible, but it would mean having to reinforce the roof structure to such an extent* that the vehicle would be massively more heavy - just to satisfy you. You might be safer from UV, but almost all UV is filtered out by ordinary glass anyway.
*Convertible cars are, perhaps counterintuitively, heavier than their fixed roof cousins - which is because they need so much structural reinforcement if their rigidity isn't to be too compromised. And the importance of the A-pillar is really shown here as it's the structure most beefed up, and most responsible for ensuring that if a convertible overturns, the occupants aren't squished.
What you are asking for here is, and I know I am repeating myself here, a Very Bad Idea. Just tell me that you don't work for a car company, please...
EDIT - actually, if you do please say which one, as I shall assiduously avoid passengering in one.