I have two desktop PCs with a single rx580 in each and I'm thinking of adding extra rx580 to both desktops but the desktops has 550watt power supply each, can extra rx580 works in both PC?
If you undervolt the cards and they can only consume like 90-100 watt each and don't use them for gaming but for mining yes it would work as I had once with a Corsair running two Gtx 1060 which would consume near the same amount of energy as Rx 580 undervolted and I mined with them.Also do not mine RVN as it consumes more electricity and it may or may not work but for Ethereum I think it will work,always with undervolted cards.
Also make sure your PSU has 2 x 8 pin connectors to support 2 GPU-s as one Rx 580 needs a 8 pin connector.
In order to avoid costly hardware failure and even fire it is best imo to build your rig with a power supply that meets the power requirments of the GPU's running at stock volts and overclocked so whatever they draw power wise when running flat out molten hot should be your calculation spec
Any error or gremlin in your rigs operating system or drivers might one day without warning invalidate any software applied under volt meaning your rig draws more power than its cheap maxxed out power supply can handle and especially dangerous if it does this in your absence for a good while.
(for me 6 x rx6800 = 300 watts =1800W plus some for effeciency power conversion takes it upto 2000W and that does not include system overhead so add another 200W for that, in reality by software under volt my GPU power consumption is half because 6 x 150W =950W but if that setting was nullified oh dear big trouble ahead if using single cheap 2000W psu).
There is also a risk thats highly likely of premature PSU failure by running close or even over its power rating constantly so avoid stressing your kit and build in some redundancy for safety and longevity. The power conversion efficiency of a Power supply will never be 100% and even 95% claims are worth questioning imo. If you have a 500W PSU it will give a safe 450W out but not all of that is on the 12V rail so proceed accordingly with long term safety and reliability of power supply in mind. More is better to avoid so for this setup 750W would be preferable.
For eg i just bought a psu claiming to be 2000W 95% platinum 8 gpu capable. yet with four GPU attached underclocked each drawing 150W the psu fan was full speed making a racket pumping out lots of heat like an electric heater and it was only pulling in at the wall socket 800W max. This psu has a label on it that i dont trust and its getting returned as unsuitable as i no way trust it to run at its claimed label rating and even if id id its to noisey, This psu is the same size and weight as a 1000W maybe with a fan mod so it can be driven harder than its rating and i dont like it im not leaving it unattended in my home knowing anyone can print a label off, right.
so back to 2 x 1000W for my 6 gpu rig and less noise n risk of fire and those paying attention should be able to point out even 2 x 1000W is slightly to low for the needs of my example if they do draw 300W max but these GPU actually run at stock volts around 240W so its 240W x 6 = 1440W + 200 for system overhead = 1640W drawn from two 1000W psu gives safe spare capacity to accommodate power conversion efficiency so as not to stress them or the rig. Also consider in time that electrical components age and reduce performance accordingly = fire.