Are there examples of strategies where a combination of third degree pricing and two-part tariffs are used together? Of course, I am only interested in instances where the combination of the two strategies ultimately lead to higher profits than if the monopolistic firm had used only one.
Here's an easy example: movie theaters.

If you view theater pricing models as a two-part tariff (ticket + snacks) then any time there's a "seniors discount" or something like it, this would fit your strategy.  It's a simple exercise to determine the conditions for profitability of such a campaign, but the fact that they've been around forever suggests that on net, they are.