Perhaps Peter (Gambalunga) will come forward on this. As far as I remember he changed his Plus 4 from 195/60/15 to 195/65/15 and was very happy with it because he gained more ground clearance.
It must be said that of all Trad Morgans, the Plus4 has the smallest diameter tyres. In 2010 MMC itself had made a change to another model. Until then the Roadster, at least the series 1, had 205/60/15 tyres on the aluminium rims. (Stainless steel spoke rims had 16 inch). With the Roadster Sport in 2010 they then changed to 205/65/15 ex works. But then to 15 inch painted spoke wheels.
In short, you can drive 195/65/15 without hesitation. You have the benefit of greater ground clearance. The gearbox is slightly longer due to the slightly larger tyre diameter. The speedometer is very easy to readjust, because it interprets the signal digitally.
But I wouldn't use wider tyres, because all Morgan wings are always cut quite precisely to the specific tyre width during construction. And the steering may feel more easy and relaxed when keeping 195 width.