4 gigs is not a likely barrier to break easily. That is the limitation of filesize for 32bit filesystems, and even though it's likely you are not using a 32 bit filesystem (likely NTFS, which is a 64 bit filesystem), many apps are also written in a way that they are limited to 2^32 bytes filesize (4GB). For example, notes mail backup files are limited to 4 gigs each as well and in my experience, Winzip won't create zip files larger than 4GB, even on NTFS file systems which can have single files significantly larger.
I'd be surprised if there is a way around it.