What I think causes many problems here is in computer land people talk about "watts" and even benchmark in "watts". However, when talking about PSU's in general, the considerations should be voltage and current. The reason is you could have in one situation low voltage and higher current, and in another high voltage and lower current; however in both the power (watts) measurement could be identical. So using watts as the sole criteria is not really indicative of the need or problem.
A "Watt" is power; a rate of energy calculation of voltage and current. Specifically a watt (W) is when one ampere (A) of current flows through an electrical potential difference of one volt (V).
1 W = 1V ⋅ A
So this means, if you have a 1 volt rail and a current draw of 1 amp the rate of energy or power is 1 watt. Also if you have 100 volts and a current draw of .01 amps you still have 1 watt. Also if you have .5 volts and 2 amps of current draw it is still only 1 watt. So to be using 1 watt of power on a 12 volt rail, you need to draw approximately .08 amps.
So you can see that power measurements can be useless in any application using a PSU. Even using power to determine what PSU to use in a given application is not wise. It only indicates the rate of total energy; it does not tell you anything more than that rate. What is relevant is knowing the amount of current drawn or required on each voltage rail.
When choosing a PSU for any electrical use, the primary factor is the amount of current that will be drawn from any voltage rail. Once you exceed (or reach a practical limit) of current draw on a given voltage rail, this is when you see voltage drop across that rail. (What I see some computer enthusiasts incorrectly refer to as "V-droop"). So what is important to understand is you must calculate the max current need for each voltage rail and choose a PSU that will deliver more than that amount current, since headroom on current (sometimes refereed to as "duty cycle") prevents issues like voltage drop and excessive heating.
Talking about power alone is pointless.
As far as the issue of running multiple power supplies (other than for redundancy applications), the issues and problems are due to the nature of how a PSU functions; how it converts wall AC voltage to usable DC voltages and current for a computer to use. Without getting too technical in how this is accomplished, most PSU designs require that the two PSU's be "linked" in some fashion. In most cases in this link, the grounds are bridged common and sections of the circuitry involved in regulation (like timing) are synced.
One of the few manufacturers making computer PSU's that offers this form of linking is Antec in the "High Current Pro" series. This is what Antec calls "OC Link". By connecting two PSU's of this series together, you can increase the total current available, and use all the connections on both PSU's in the same computer without any worry of problems. I am sure their are other manufacturers who offer this type of linking, however this series by Antec is the one I know of at this writing.
When using two PSU's in the same build it is important to understand that it is not sufficient (or safe) to simply connect two PSU's together or even to use some third-party "external device" alleging it can safely connect PSU's together externally. The linking of two PSU's must be internal, built-in as a feature and is proprietary to each design type of PSU.