There is a long interminable sticky thread on this subject at the top of the forum.
My view is that the need to increase contrast as print size goes up is largely perceptual. There isn't much physical effect with modern enlargers and lenses when combined with a blacked-out (or redded-out) enlarger alcove.
AA had a terrible time getting contrast on his mural prints. They were 5x7's - but measured in feet. The reason does seem to have been stray light. His darkroom was painted white and the enlarger was homemade, with an unknown amount of light leakage. And the lens wasn't multicoated.
If physical effects are contributing to contrast loss then:
Stray light from the enlarger can be dismissed (unless yours leaks like a sieve). The greatest stray light source is lite bouncing off the paper. The second greatest contribution is stray light from the lens - peer up at the lens and you can see quite a bit of illumination that shouldn't be there. To see the enlarger proper's contribution you can make an experiment: Turn on the enlarger and look at the illumination on the walls, then cover the lens and look at the contribution of light leaking from the enlarger; it's not night and day, exactly, but the enlarger's contribution to total stray light is tiny in comparison.
A lens hood on the enlarger might not be a bad idea. A multicoated lens will also reduce stray light.
If the aperture is opened to compensate for larger print size then printing time stays the same and the fog from the enlarger and the lens doesn't change.
The greatest contribution to lowered contrast, fog from light bouncing off the paper, will increase with print size: this was probably AA's greatest contribution to reduced contrast. The total amount of light from the lens is constant with print size, assuming you are using time to compensate. A certain percentage of the lens output bounces from the paper, then to the walls and back on to the print. So the total bounced light is independent of print size. However, as print size increases the exposure time increases and thus the effect of this bounced light increases. Using the aperature to compensate won't help here: if you open the aperture then the amount of bounced light increases (more total light).
Painting the walls and ceiling around the enlarger matte bright red (or black) is the only way to mitigate the effect of bounced-light fogging. It also reduces any effects from stray lens and enlarger light.
Reciprocity failure increases contrast. It's the same with paper as it is with film, but rather than the shadows going empty it's the highlights.
Using an EM-10 requires that you use the lens aperture to compensate for print size. If you are using an EM-10 then it is a good idea to make your work prints at a small aperture, so that the lens is at optimum when opened up to make the final print. The EM-10 was designed for use with Ilfochrome printing, where changing the exposure time would shift the color balance. There is another company (cough) that makes a meter better suited to this purpose, this meter has 1/100th of a stop of resolution and can meter any contrast changes accruing to the larger print size.
My experience is that small work prints are fine if they are no more than 1 size smaller: 11x14 for a 16x20, say. But that is still reducing paper wastage by half.