Why not!
There is nothing stopping you or anybody, even on a temporary visa to own and run a business!
Yes, what might be an issue is whether you can get paid from your business.
As far as I know, you can take profits from your business, but not get a fixed paid salary. (you cannot get employed, if you are not a permanent rez.)
In case of your wife, she can start "working" for her business, once she gets her EAD.
EB2
