If you're allowing access to the Time Tunnel, then another show, which actually ran concurrently with batman 66 was Wild Wild West (ran 1965-1969).
Featured a similar "camp" tone, with an endless cast of character villains and over the top gadgets action and plots.
James West and Artemus Gordon as counterparts to Batman & Robin.
West even had a butler/valet in Tennyson.
And they had their own version of Commissioner Gordon calling them to action with Colonel Richmond.
They can load the Batmobile onto the tracks with the Wanderer (pretty much their traveling batcave with crime lab).
Analogous to the Joker Penguin Catwoman trio they have - Dr. Miguelito Loveless, Antoinette & Voltaire, if you want to make it four with Ridler, add Count Carlos Mario Vincenzo Robespierre Manzeppi.
The meeting of Loveless and Penguin alone and them plotting together would be brilliant! All these colorful villains would make such a great team-up.
And if they really want to tie it all together make Artemus Gordon the great ancestor of James Gordon.