Extra fats will keep the crumb tender but can somewhat retard gluten formation and effect rising.
I like adding eggs too. Eggs added to dough help with rising. A bread dough rich with egg can rise very high and fats from the yolk help to tenderize the crumb and lighten the texture a bit. Eggs also contain the emulsifier lecithin. Lecithin can add to the overall consistency of the loaf.
Replacing part of the water with milk gives a more tender, sweeter bread as milk sugar (lactose) is not eaten by the yeast.
Salt slows down fermentation and enzyme activity in dough and leaving out of bread, especially machine bread, can cause the dough to blowout and collaps. While salt boosts the flavor of the bread, it also tightens the gluten structure and strength of the dough increasing the the carbon dioxide gas retention during fermentation giving better volume.