You must ignore the effects of contamination of the product from the stainless steel plate as a counter electrode during water oxidation/oxygen reduction reactions (in basic media).   The counter electrode is to provide the location of the second electron transfer reaction. For the electrolysis, to avoid the contamination of the product from the counter electrode, it is arranging separately, isolated in a chamber, from the working electrode. For electrochemical measurements such as cyclic voltammetry, because of the short measurement time, you can ignore the effects of contamination by electrolysis. However, in the case of bulk electrolysis, because of long measurement time, the agitation and separation of the working electrode and counter electrode using a chamber is necessary, to prevent the transportation between two electrodes for the contamination of the product from the counter electrode.

You must ignore the effects of contamination of the product from the stainless steel plate as a counter electrode during water oxidation/oxygen reduction reactions (in basic media).   The counter electrode is to provide the location of the second electron transfer reaction. For the electrolysis, to avoid the contamination of the product from the counter electrode, it is arranging separately, isolated in a chamber, from the working electrode. For electrochemical measurements such as cyclic voltammetry, because of the short measurement time, you can ignore the effects of contamination by electrolysis. However, in the case of bulk electrolysis, because of long measurement time, the agitation and separation of the working electrode and counter electrode using a chamber is necessary, to prevent the transportation between two electrodes for the contamination of the product from the counter electrode.

Thank You Prof. Shen-Ming Chen. 

I have commonly used a hollow stainless steel tube as counter electrode in a flow system and basic media (not as much as 0.1M KOH) without problems. It is true that it was downstream the WE, but now I use stainless steel pins for counter electrodes and it is fine. I pay attention to have enough area for the electron transfer.

Stainless steel plate will be OK while used as cathode. Depending on CD, it could have some corrosion issues when used as anode...

following good answer from Shen-Ming Chen,

we must, also, consider that stainless steel is not a single (unique) material, but a member from a BIG family[1].

1. ASTM's steel standards https://www.astm.org/Standards/steel-standards.html https://www.astm.org/DIGITAL_LIBRARY/MNL/SOURCE_PAGES/MNL61.htm

I 'm not sure if I ever encountered it in alkaline solutions, but I observed leaching out of iron in some electrolytes in bulk electrolysis. I didn't investigate it further.

Does anyone has experience with low-iron types of Hasteloy or Inconel stainless steel as an anode?

I agree with Juan and Ionnis for sure.  Another facxtor:  As long as the stainless steel electrode is much larger than the working electrode, to keep the current density at the counter electrode low, there should be no problem.  Platinum is used for many things because of tradition for 100 years, not because it is needed very often. There are many other possibilities such as various forms of carbon. 

Stainless steel can be used as a cathode for water electrolysis.  However if you use it as an anode in KOH solutions and if the solution is hot (~60C) you will notice iron going into solution as a ferroate anion. The solution will also be contaminated ( and may turn brownish).  In any case stainless steel is not great since its resistance is fairly large.  In the industry nickel anodes and mild steel ( low carbon) cathodes are used.

If use Stainless steel as anode that lead to contaminate your electrolyte due to corrosion of S.S. You can use just as cathode.