Hi,
Yes, this is possible by assigning the privilege to user. I have mentioned the steps to create the privilege and assign to user.
Here it follows,

How to create the privilege:
Navigate to Setup --> User Management --> Application Privileges
Click New. Provide privilege name
Uncheck the My Items under Tab and Form Privileges.
Click Check In.

Note:
Under Object Privilege, check the insert, update and delete option based on your requirement

How to assign the privilege to user:
Navigate to Setup --> User Management --> Application Users
Select Add a user, under privilege details click on Zoom button, select the privilege
Click save.

Note:
For Administrator, Navigate to Setup->personalization, select My Items and click on Remove selected items.