I would also add that, should you put a DC/DC converter between the UPS and its batteries you bypass the battery undervoltage protection built into the UPS. You could therefore damage the batteries by discharging them too far without noticing.
That is not necessarily the case.
Instead of trying to design a regulating 3 kilowatt switching power supply to convert 4x12V to 10x12V, it would be much simpler to design a 3 kilowatt inverter. Open loop operation means that the output voltage will track the input voltage minus losses. An inverter also places fewer demands on the input and output capacitors.
Now the big problem becomes finding or building a suitable medium to high frequency transformer. If I did not wind the transformer for 20+ kHz operation, then I would use several 60Hz transformers in parallel at a slightly higher frequency if I could find the right voltage and ratio.