Is upping the voltage on a multiplexed LED display an appropriate response for dimness?
To increase brightness of a multiplexed display, the current through each LED segment needs to be increased (to a limited extent), while ensuring that the average current and power ratings of each LED are not exceeded. It isn't about raising the voltage to the LEDs.

The current may be limited by either a constant-current driver, resistors on each LED, or a resistor array serving multiple LEDs. Changing this current limiting mechanism can be done, but is not for the faint of heart. Also, the display then will be unsuitable for direct (non-multiplexed) drive, as the LEDs would blow due to too much current.

Alternatively, if resistors or a resistor array have been used, the voltage source feeding these resistors could be increased, thereby increasing current through the segment.

Also, keep in mind that increasing the current through an LED significantly over the rated current, for however short a period, can have detrimental or outright destructive effect on the LEDs. See this answer for further insight into this. 

Another approach that merits investigation is whether the multiplexing algorithm is optimal, as in, is it keeping individual segments lit as long as it can per cycle. If not, then software fixes can improve the brightness somewhat.