I noticed in the Bewitched series they remade some black and white shows in colour.
Gilligan's Island didn't have remakes but I'm sure elements of the plot for "Angel on the Island" became season two's "Castaways Pictures Presents" and season three's "The Producer"

In The Second Ginger Grant, due to a head injury, Mary Ann puts on a show of being Ginger.So Ginger must put on a show of being Mary Ann.

In Voodoo Something To Me, to cure Skipper of a superstitious curse, Gilligan puts on a show as a witch doctor.

In The Matchmaker, Mrs. Howell misses opera and seeing Gilligan and Mary Ann as Romeo and Juliet, connives to fix them up so she can have a show.

In The Postman Cometh, to help Mary Ann get over a boyfriend who they hear on radio got engaged to someone else, the men romance her as Charles Boyer, John Wayne and Cary Grant.

In Not Guilty, a radio report says one of the 7 killed a guy in Hawaii right before the cruise. The only way to allay suspicion is to put on a show re-enacting the crime ala Perry Mason.

Plus all the dream sequences, they put on a show parodying High Noon, Dracula, James Bond, Cinderella, Errol Flynn pirate movies, Dr. Jekyl and Mr Hyde, etc.

I was being a little more specific than that. Mainly, Mr Howell being a director and the castaways performing a Shakespearian play for Ginger's benefit.