The agitation during the development process is to replace the exhausted developer on the negative surface with active developer that is not in contact with the image surface yet, making it developing faster. Specially the highlights which is the most active part of the negative development.
During film development the less dense areas in the negative (meaning the dark or shadows areas) are first developed, and sfter a while it will not have much effect during the development.
So the agitation and timing on traditional film development is to control the more dense areas (meaning the bright areas) which takes longer to develop and will quickly developing further when agitated until blow the highlights up if the process is not interrupted on time.
Stand or semi stand development is different. It is about have just enough developer concentration for the images development, and leave the film in the solution undisturbed (stand) or with minimal agitation of the solution during the process (semi stand).
When the negative is left in the developer uninterrupted or with minimal agitation, the solution in contact with the highlights (more dense and active area of the negative) will fast be exhausted, and the idea to leave it standing with no agitation is to avoid replacing this exhausted developer with active or fresh part of developer not in contact with the surface yet. So you can leave the negative in the solution for long time and the highlights won't continuous developing any further.
On the other hand, the less dense area of the image on the film negative (shadoes or dark areas), are less active areas of the image during development process and for this reason these areas will not quickly exhaust the solution in contact with its surface. So theses dense and less active areas will slowly keep developing further, brightening the shadows details.
This also means that stand or semi stand development takes longer. Usually and in most cases about 1h. This is how we get more tonalities through stand or semi stand development.
An other aspect of the standing development is the sharper look dues to "Edge Effect". This edge is the line between brightness and shadows. In other words, it is a micro local contrast caused by developer exhaustion and circulation in a micro scale during development process.
It has a down side though. Many people complain about the uneven image brightness from stand development, specially with middle and large format negatives. For this reason many people opt to do semi stand development which consist on agitate once, twice or three times during the process, because the uneven result is caused by the concentration of developer on the bottom of the tank when the solution is not agitated for too long (1h for example). Some others claim to solve the uneveness result by pre soaking the film for a couple of minutes in whater that has the same temperature of the developer, because high variation of temperature seems to also cause this problem.
Standing development also delivers bigger grain which may not be everybody taste. From my part, I love grainy images.
I don't know id the stand development is possible with any developer. What I know is that is is most used with HC-110 and specially Rodinal. A good thumb rule to start is to use 1:100 Rodinal dilution and develop for 1h, for the film negative box ISO speed. From this start point you can experiment and results you like the best.