I do not think so, if they are started by the same user.
But, you can create a standard user with limited rights. Then edit permissions for that file, so this particular user will only have right to Read and/or execute.
But now you will have to start ONLY that program as that standard user, but because you will be initially logged as normal user, other programs will be started normally and have different permissions for the same file.
Let me know, I can create a bat-file to start program as another user, which will look like this
Runas /user:johnDoe "C:\myfile.exe"
Or you can start it with Right click menu, but you need to modify it first using this tutorial.