There are two possible solutions which make sense here, depending on the trade offs you would rather make.
National Instruments has a SCXI-1127 multiplexer (MUX) module which has 32 differential (2-wire) channels. With this solution, you would need exactly 15 SCXI-1127 modules, which can be cascaded to act as one large 480:1 MUX. To house the SCXI modules, you will need 1 SCXI-1001 chassis and 1 SCXI-1000 chassis. The SCXI-1000 and SCXI-1001 are the same except the 1000 has 4 avaliable slots and the 1001 has 12 available slots, giving you a total of 16 available slots. You will also need 15 SCXI-1331 connector blocks, which are the equipment which connect your batteries to the switch modules. The 15 switch modules, 15 connector blocks, and 2 SCXI chassis will effectively act as one large 480 channel MUX for your batteries.
The other solution is similar, but makes use of the SCXI-1129 high-density matrix switch. One SCXI-1129 matrix module and one SCXI-1334 connector block create a 4x64 (row x column) matrix. Eight SCXI-1129s and SCXI-1334s can be cascaded to create a 4x512 matrix which could route all your batteries to the same measurement device.
The SCXI-1129 is more expensive, and this application doesn't really require a matrix solution, but the saving here is in real estate since you only need one SCXI-1001 chassis to house the 8 modules. The SCXI-1127 solution is less expensive and uses a true MUX approach, but requires more physical space.
Both solutions will also require some method of controlling the SCXI chassis. You can use a NI 4060 DMM from National Instruments to measure (with 24 bit, 5.5 digit accuracy) the voltages that are being MUXed with the SCXI switches. The NI 4060 DMM integrates well with the SCXI-1127 and SCXI-1129 switches and can do hardware handshaking with these switches to automate the scanning and measuring of the batteries. If you plan on using a different device to make your voltage measurements, you still need a method of controlling the SCXI-chassis, but you can use the low cost NI 4021 to accomplish this. In both cases, you can use one NI 4060 or NI 4021 to control one or more SCXI chassis.