H4 to H1B conversion that do not fall under the quota

Hi,

I am currently on H4 visa and was checking for options to work. In your article u have mentioned that there is a possibility that university apply for H1B visa that do not fall under quota. Is that possible only by university or any consultancy as well can do that?

These are called cap-exempt H-1s and only non-profits like universities, schools, hospitals etc can file for it. A for-profit entity like consultancy cannot file for it.