I need to build up my attic framing for three reasons, but first, I can think of two ways in which to do this.
I would be stacking the new joists directly on top of the old joists. In theory, this should make them similar to 2x8s (I know this isn't quite true, and I have the beam theory to prove it).
I would be stacking the new joists across the tops of the old joists. In theory, I've made a lattice structure of sorts.
I am going to lay 2x4 fiberglass insulation in the original joist bays, but that only gets me ~R-13, and the guideline for my region is >R-30. Blown-in is not an option I am considering, by the way. I've heard that laying rolls/batts perpendicular to each other when stacking them is the appropriate method, so method 2 seems to make sense for this application.
Right now, when I need to do work in my attic I need to tiptoe along the tops of the joists. There is no flooring of any kind. I want to fix that situation by laying down some OSB (in some places, at least). I don't think the method I use will affect this, but there is one double-wide joist bay (there's a wall under it but no joist) so I need to add some perpendicular reinforcement there anyway, so method 2 seems to make sense again.
I am adding some cabinets that need to hang from the ceiling as sit quite far from any walls. I expect the cabinets and contents to weigh ~400lbs, and I don't doubt the existing joists could take the load (they have a 160" span), but I'd rather reinforce the framing. I had considered sistering joists where the cabinets would be mounted (method 0, not shown), but I think methods 1 and 2 effectively supersede sistering. Method 1 will increase the effective joist stiffness and strength while method 2 will distribute the load across multiple joists. I'm not sure which is better in this case.