Yes. Here's how to set a separate sudo password:

Assume your primary user account is called "user".

Set up a second account, whose password you want to be your sudo password. Let's call this account "admin".

In /etc/sudoers:

  Defaults:user runas_default=admin
  Defaults:user runaspw

Now, as "user", you can

  sudo -u root whoami

and you will be asked for "admin"'s password.

The only downside is that "root" is no longer the default user to become, you have to explicitly specify it.