OK, I would like to add some possible options to this idea to enhance this proposal, and if you like the suggestions Lord Korto, maybe you can edit the your post to include it.
One method to select multiple items would be the above mentioned method. Another would be when you open a container, you have a little check box in the upper left corner of the item that allows you to select it along with other items, similar to the way you select multiple files in MS windows explorer.
From here, along the bottom border of the open container there could be a button labelled "Move To..."(which would act like the cut option in MS Word) then open another container that would have a "Move Here" button (like the paste option in MS Word), and the items would be transferred from the first container to the second. There would obviously need to be a time limit of how long the items would remain in memory. I would suggest 5 minutes or until the items are transferred to the second container, whichever happens first. Should someone lose connection to the game while in process of the transfer or not "paste" the items into the new container, the items would revert back to their original container so that nothing is lost via that interrupted connection or inaction.
You could also use the drag and drop method we currently use for single items but allow for the multiple items to be dragged.
Another possibility would be when you hit the "Move To" button, you would get a drop down list of containers your character is in range of and that you have admin rights to. If you are near a bank terminal, your safety deposit box would also appear in this list. Should the target container not have enough room to accommodate the transfer, an error message would appear saying "That container does not have sufficient space to accommodate the transfer", and the transfer would be cancelled.
Another button besides the "Move To" one would be a "Destroy" button. Once you choose this option, you will receive a warning "You are about to destroy..." and show a check box list of the items in danger of being destroyed. That way if there was an item that shouldn't be there, you could uncheck that item and then proceed with destruction.
You could take this destruction concept further and change the "Destroy" button to a "Recycle" button instead. This would convert items into some sort of tokens that would stack. These tokens could then be used to purchase items from a new Recycle vendor or use the current Junk vendors. This option could offer things like deco items, low quality resources, lootable low level schematics and so forth. Obviously this last part is a completely different idea, but it would make the things we often destroy to make inventory room finally worth something.