Not at all. You could go to 5W30 from 5W20, but going to 10W is definitely not a good idea. You could go 0W30 if you like.
My point was that before deciding on an appropriate oil, you should compare the PDS (product data sheets) and choose a product with superior specifications (e.g., flow characteristics) to OE. Higher flash points and lower pour points, for example. BTW, a higher viscosity index means a higher resistance to viscosity change/shearing under standardized conditions. That is a good thing. BUT we don't want to significantly deviate from the viscosity itself as specified by OE.