You can backup to multiple files and restore these files with backup compression these files should be a lot smaller then your databasesize.
Example
BACKUP DATABASE [YourDatabase] TO
DISK = N'\\YourDriveOrNetworkFolder\YourFOlder\MNGDB_2.bak',
DISK = N'\\YourDriveOrNetworkFolder\YourFOlder\MNGDB_1.bak',
DISK = N'\\YourDriveOrNetworkFolder\YourFOlder\MNGDB_3.bak',
DISK = N'\\YourDriveOrNetworkFolder\YourFOlder\MNGDB_4.bak'
WITH NOFORMAT, NOINIT, NAME = N'YourDatabase-Full Database Backup', SKIP, NOREWIND, NOUNLOAD, COMPRESSION, STATS = 1
GO
You cannot restore one file at a time, you will need to have all files.
You can however restore from multiple backupfiles (if you have taken a backup to multiple files) which can be located on multiple disks or network locations.
Example
RESTORE DATABASE [YourDatabase] FROM
DISK = N'\\YourDriveOrNetworkPath\YourFOlder\MNGDB_1.bak',
DISK = N'\\YourDriveOrNetworkPath\YourFOlder\MNGDB_2.bak',
DISK = N'\\YourDriveOrNetworkPath\YourFOlder\MNGDB_3.bak',
DISK = N'\\YourDriveOrNetworkPath\YourFOlder\MNGDB_4.bak'
WITH FILE = 1,
MOVE N'YourFile' TO N'\\YourDrive\YourFolder\YourFile.mdf',
MOVE N'YourLogFile' TO N'\\YourDrive\YourFolder\YourFile.ldf',
NOUNLOAD, STATS = 5
It all depends on the size of your backupfiles & the size needed by the datafiles & logfiles to be able to say if it is possible or not.