Hi @Ilya_Golubtsov and welcome to the Forum! 
As it stands, each task can only have one assignee, this is to ensure it’s always clear who’s responsible for completing the work You can learn more about this here .
You can always add collaborators to the task, so they can stay informed of the task progress.
If you’d like to create the same task for multiple people, you can easily create copies of a task and assign them to each individual by following these steps: Asana tasks - understanding the basics | Product guide • Asana Product Guide (scroll down to - Assign Copies)
You can learn more about Tasks in this handy article: Task actions: create, move, duplicate, and more | Product guide • Asana Product Guide
You can also set a due date, due time, or date range to let the assignee know when a task should be completed by. When the task is approaching its due date, a notification will be trigger to the assignee. You can learn more about it in the following articles:
I hope this helps! Please let me know if you have any follow-up question!