Okay, I’m thinking Data would fill the lead role. Add an amped-up emotion chip and a leg injury from a Borg battle. Data has always been able to swoop in at the eleventh hour to save the day. Now he struggles with random white-hot emotions that cloud his otherwise cold logic. Data also has an obsessive unfulfilled quest to be human, which is like House’s quest to fix his leg.
Geordi would be Wilson. Bachelor and uptight straight-man who is good at his job and prone to pranking.
Riker would be Foreman, Thirteen is Beverly, Chase is Wesley, Masters is… Troi?
Leaving Picard as Cuddy. But that means Data must eventually seduce Captain Picard and brag about the sexual conquest to the crew.
Also, each week, they take several approaches to completing their mission, including phaser stunning random innocent people who might be involved in the plot because it is faster. They would also routinely transport into people’s homes or quarters without permission and take things to help with their investigation.
Every so often, Data would ask Picard to blow up a random starship. Picard would balk at first, but eventually acquiesce. It’s a coin flip as to whether the random starship of the week needs some explodin’, but sometimes Data has a last-second insight that saves an innocent starship from needless annihilation.