Opening a stored procedure file multiple times in sql server management studio
No, there is no such option.

SSMS doesn't open the database object and lock it down for you like Visual Studio w/ Data Tools add on does. Instead, it generates a sql script depending on what you want to do. It is more of a "Oh, you want to modify 'dbo.sp_awesomeness'? Not a problem! Here is the sql script containing alter procedure code you need at the time you asked of it." 2 minutes later, you ask again, and it pops open a new window going thru the same as above. It is always giving you the information at the time of the request to SSMS.

Visual Studio does the "Oh hey, you want the dbo.sp_awesomeness! Sweet. I see you checked it out of git hub, that's all good. Here is the copy." When you ask for it two minutes later, it just brings up the original screen. But then again, you are not creating sql scripts from SSDT. You are building a database package to deploy.