Hi,

Yes you are right , some colleges get done with their processes by then. But even after May, you will get calls from private Bschools and management institutions ;especially for direct admission. 

However do check the site of ATMA for list of colleges accepting MAT scores for MAY exam. you can choose the college of your choice. Attaching a link.

https://www.motachashma.com/entranceexam/200855/mat-participating-colleges