If you mean legacy backpack for your own inventory, plus grid for corpses/chests, then yes.
Close your inventory pack
User Settings>Legacy>Legacy containers ON
Open your inventory pack
User Settings>Legacy>Legacy containers OFF
As long as you keep your own pack open, it will remain in legacy view.
Corpses and containers each may use either grid or list view as specified in User Settings>Options.
Someone more familiar with Command scripts will probably be able to write you a short macro that does the quoted actions in one button press.
OR
If you meant a legacy-style backpack with gridded contents, then I believe there's a mod for it.
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Other notes:
Treasure chests count as containers rather than corpses, and as such must be looted by dragging rather than rightclick.
Dropping an item into a Grid view cell places it in roughly that same position in Legacy view. Top left = top left, middle right = middle right, etc.
Dropping an item anywhere in Legacy view, or onto a container, will place it in the uppermost available spot in Grid view.
List view arranges things in the order they were added to the container.
In Grid view for your own inventory, you can place items you don't need to browse down the very bottom of the grid. I do this for items I already have on hotbars or bound to keys (eg: runebooks, potions, etc). Also you can position all your paperdoll gear such as armour or weapons down the bottom. When you disarm/unequip them, they will go back to that slot out of the way of looted items, etc.
