Unfortunately, you can't "raise" the operating voltage of an IC above the maximum that is given in the datasheet, in this case 5v. It appears that the input voltages to be measured are constrained to also be in this range, i.e. no more than 5v, which is what is causing your problem.
You have a couple of options: if you want to measure just the voltages, but no currents, you can use voltage divider(s) as shown on the right side of page 18 of the datasheet. If you need to measure current also, they show a circuit on the left side of the same page, using a separate current sense monitor chip (LTC6102HV) which adds lot of complexity and cost.
Instead, I suggest using a voltage/current monitor IC designed for higher voltages, such as the ISL28022. It can measure voltage and current over a range of 0-60v. It doesn't include a temperature measurement function, but I2C temperature sensors are a dime a dozen (well, maybe not quite that cheap, but this one -- LM75B goes for 60 cents).