Possibly, but not the standard formatting that Windows will do.
You might have to increase the cluster size. This will have a negative impact though. if you have a 1KB file it will take up a whole cluster, which to do 4TB would be 64KB per cluster?
Is exFAT an option for you?
Interestingly, Microsoft doesn't even list what you've already achieved as possible:
Default cluster sizes for FAT32
The following table describes the default cluster sizes for FAT32.
Volume size | Windows NT 3.51 | Windows NT 4.0 | Windows 7, Windows Server 2008 R2, Windows Server 2008, Windows Vista, Windows Server 2003, Windows XP, Windows 2000 |
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7 MB–16MB | Not supported | Not... | |