Hi

I don't think there is any limit to the number of domains you can set as long as you are following the nesting rules and have adequate computing and memory resources. However, often new value wouldn't be added to your simulations after a few nests. This may be because the model couldn't capture realistic atmospheric waves at the microscale given the lack of high resolution geographic data (topography, land use, soil categories ).

Hope this helps!

Tabish

Tabish, above, is largely correct: care should be taken in adding more and more nests to your domain, as it is a game of diminishing returns. Also, increasing resolution puts additional importance on your selection of a priori. 

You may want to consult a few of the papers below:

For computational concerns: http://link.springer.com/chapter/10.1007%2F978-3-642-32820-6_80

For benefit of nesting in tropical storm situations (nowhere near as extreme as what you are suggesting, but it's a start): http://onlinelibrary.wiley.com/doi/10.1029/2008JD011623/full

Benefits of increasing resolution: http://journals.ametsoc.org/doi/abs/10.1175/1520-0477(2002)083%3C0407:DIHRPM%3E2.3.CO;2

Thank you very much for the quick response Tabish and David!

Actually, my concern is not about increasing resolutions. It's about having one very large first domain, having 3 second domains, and within those 3 domains, are sub-domains and so on. The finest resolution is 2 km but very many child domains with all domain numbers exceeding 20.

Hello,

Think you already got your answer. As long as you have a great computer resource to back the model up, you can use nested domain (even with different parent domains) as much as you need in WRF. But be careful about the estimated time. As every nested domain will ask for feedback data from their respective parent domains.

here is the forum link of nesting domain you might find helpful

http://forum.wrfforum.com/viewforum.php?f=10

http://www.dtcenter.org/wrf-nmm/users/OnLineTutorial/NMM/Nest/run_wps_nest.php

No matter what ever is the resolution you use beyond a certain limit the advantage you get in a fine mesh model has some limitations. Since the whole globe is of the dimensions 360 by 180 degress  if you maintain the 3:1 ratio it cannot be less than a minimum.