Connecting two PSUs in series and parallel
For that type of power supply it should be ok to parallel or series  multiple devices to obtain more output.
IHA0109D05 Datsheet
As you can see from the graph on the top of page 4 of the datasheet the output voltage droops significantly with increase in load. This will allow the two units to share the load current.
Because of unit to unit variations two units in parallel will probably not share the load equally which will mean that you won't strictly get double the power output. If you had two units at the extremes with one at the high limit and the other at the low limit it could be as bad as a 10-90% split (eg if one was 5% high at full load and the other was 5% low at 10% load). It is extremely unlikely that would occur though.
Another point highlighted by @user263983 in the comments is that the graph is shown as &quot;Voltage Accuracy&quot;. My interpretation of that is the graph is meant to cover all models of the device with varying voltage and current specifications.
If it included a regulated output where the output voltage remained constant they probably wouldn't share the load evenly when paralleled and the one with the slightly higher voltage would take al the load until it reached its maximum current, depending on how it responded to this overcurrent it might overload and fail while the other supply is doing nothing.
These supplies are commonly just a simple two transistor oscillator feeding a transformer with a bridge rectifier output, no regulation is provided.
One comment - the datasheet indicates the isolation voltage is 6kV not the 16kV that you state.