Yisela's answer is good and, in the event of a non-negotiable no-plus-can-be-used restriction,
is probably your best option.
In the absence of such a bizarre restriction, you really shouldn't try to be too clever with icons. Plus and minus signs have been used for hundreds of years to represent "more" and "less" respectively. When used in a mathematical context, plus means addition.
Since your "Add new" action is representing doing addition - be it adding an object, or adding to an object, or whatever - you simply cannot get a stronger and simpler visual correlation than the mathematical sign for addition..
Usually the "new generation of {historic icon}" questions involve imagery that is considered outdated or that may not be immediately intuitive to new users. A floppy disk for saving, a pencil for editing, etc. Replacing these images makes sense because people don't use floppies at all and may not use pencils regularly. The plus sign will probably mean "addition" until the end of time, and can be represented clearly in as little as 9 pixels - it's silly not to take advantage of that.