A new backpack upgrade would be nice, but the problem i find i have with the backpack more often than not (after buying all the upgrades) is the fact that some things don't stack. Like Fishing Tackle, weapons and accessories. The amount of times ive gotten fishing tackle, accessories and weapons from treasue chests while fishing or fighting monsters is unreal. But because they don't stack, they end up clogging up my inventory and forcing me to return home prematurely or dump stuff to continue exploring.
When my inventory isn't being clogged up by the things that don't stack, i tend to find that my backpack is big enough. When i do things like fishing, Ginger Island exploring or dungeon delving, i only take items that i will need with me.
For example
When i go to the desert mine i only take my weapon, pickaxe, 1 type of food (with a buff to compliment what im going there for), 1 type of bomb, and either the return sceptre or farm totem.
The only time my inventory ever cloggs up after i buy the huge backpack, is when i pick up a few non stackable items in one go. My backpack tends to be big enough to carry the amount of stuff that i find in any one day most of the time.