There's no basis for increasing the viscosity. There's also no harm in doing it either aside from a miniscule change in fuel efficiency (if any) and a tad higher operating oil temp (from increased hydrodynamic friction). If the engine has clearanced itself excessively to the point of warranting a viscosity increase, something is already terribly wrong. Contrary to popular belief, the operating oil temp doesn't vary significant enough with ambient temperature to warrant a change in oil grade. The oil simply doesn't care as much if it's 20°F or 100°F outside when it's surrounded by 200°F coolant, passing through 275°F bearings, and splashing on 450°F cylinder walls. Load has a much more significant impact than ambient temp on the oil's operating temp.
I don't like the idea of 10W-40 as it's an oddball grade these days. Conventional 40 grades are usually 15W-40, synthetic 40 grades are usually 5W/0W-40, and 10W-40 is just this oddball in the middle. As such, they tend to not get very much attention, much less R&D. The exception is a specialty oil requested in that specific grade such as HPL's No VII Euro 10W-40. The only reason that grade is still available is because it's still selling sufficiently enough to people who still think it's 1975. The majors on the store shelves are in a race to the bottom. They're going to formulate the oil as cheap as they can possibly can for a given standard as that gives them the opportunity to underprice a competitor at the same or better profit margin. The wider spread grades actually tend to be better at high operating temps and loads as it forces them to use better quality base oils and VII to meet the spread. With that better quality comes lower volatility, better shear stability, and more oxidation resistance. This applies to common store brands, not so much boutique brands.
If you insist on using a 40 grade, I would recommend Mobil 1 FS Euro 0W-40 as it's the best bang for the buck off the store shelves. It's better in pretty much every parameter compared to that 10W-40.
My Tahoe has ~286k miles and still on 5W-30 oil at 15-20k mile intervals. My Nissan hardbody has >480k miles and still on 5W-30.