I want to apply for a PhD. I applied to 2 universities before and got rejected. Is it OK to send my PhD proposal to multiple universities at the same time in the hope that I get approval from one of them?
Yes it is OK and normal to apply to multiple schools.
But you should tailor your PhD proposal for each application so that you explain why you would like to study in the specific environment offered by that school (e.g. particular academics you would like to work for, courses you'd like to take etc.).