From just the equipment point of view:
Primary issue would be EMI from one device affecting the other. The could occur due to proximity of the units themselves or via the wires to the charges/batteries.
While this could be an issue you would find this in ground testing, with all systems active and setting off real ematches EMI wise the system will be very similar to in the air
Due to the differences in the units (Hardware and/or algorithms), while they are set to operate at different times/altitudes they could operate at the same time. With both charges being activated at the same time the rocket could over-pressurize (like - blow up).
The time frame for the ejection charges is in milliseconds, this is statistically very unlikely to happen. If you throw two darts at a target with 2000 possible locations determined completely random, what are the chances the two will hit at the same spot? Plus thisd wouldn't even been an even distribution like that, only the overlap time would be possible.
Minor risks could be a part from one falls off due to G forces and hits the other.
If you mount the altimeters per the instructions (Usually 4 4-40 screws) properly you would have to be pulling serious G's to cause those to fail.
Combined heating from the two units could impact operation - although I would think thermal heating from the sun would have a much greater impact
Mass of one unit versus two would change the resonance frequency of the sled which could cause a problem.
Most of these are running processors that are using less than 2 watts, these things will run on tiny batteries for hours. Overheating is not an issue, ambient airflow will be more than enough to prevent heating.
May be other failure modes.......
There are always other failure modes. That's why redundancy is important, a one point of failure system get increasingly unacceptable as danger from the rocket increases (complexity and size)
Then from the human/operator issue, (which I believe is a bigger concern....)
Having more units means more wiring and complexity which can lead to erroneous connections (such as accidentally connection the main charge to the drogue channel).
Different units typically need to be set/programmed differently which could lead to errors.
These are absolutely the number one cause of errors, the correct solution is to properly checklist and verify working conditions pre-flight.
And since most units beep out continuity or other info having 2 units could make hearing one over the other a problem
You should be at the very least able to turn one altimeter on, check it, turn it off, turn the second on and check it then turn the first back on. In my case I turn the stratologger on and wait for continuity beeps, then turn on the Telemetrum and look for my phone to connect and verify continuity.