Hmmm....
The Muppet Movie has (Rainbow Connection, the dance Kermit and Fozzie do at the El Sleezo, Movin' Right Along, Can You Picture That, Never Before Never Again, I Hope That Something Better Comes Along, Fozzie's "America", the quick Movin Right Along reprise, and The Magic Store (finale)) In total: 9 song and dance numbers
The Great Muppet Caper has (Hey a Movie, Happiness Hotel, Steppin' Out With A Star, Nightlife, The First Time It Happens, Couldn't We Ride, Miss Piggy's Fantasy, and Hey A Movie reprise (finale) ) In total: 8 song and dance numbers
The Muppets Take Manhattan has (Together Again, You Can't Take No For An Answer, Saying Goodbye, Rat Scat, I'm Gonna Always Love You, Right Where I (We) Belong, Somebody's Getting Married, and He'll Make Me Happy) In total: 8 song and dance numbers
The Muppet Christmas Carol has (Scrooge, One More Sleep Till Christmas, Marley and Marley, When Love is Gone, Christmas Scat, Bless Us All, Thankful Heart, and the Finale) In total: 8 song and dance numbers (9 if you wanna count Fozziwig's Party, and 11 if you wanna also count Room In Your Heart and Chairman of The Board (The cut songs from the movie) )
Muppet Treasure Island has (Shiver My Timbers, Something Better, Sailing For Adventure, Cabin Fever, A Professional Pirate, Boom Shakalaka and Love Led Us Here) In total: 7 song and dance numbers
(Not counting Muppets from Space)
The Muppets has (Life's a Happy Song, Pictures in My Head, Moopets Rainbow Connection, Me Party, Let's Talk About Me, Man or Muppet, Smells Like Teen Spirit, Forget You, Rainbow Connection, The Whistling Caruso, and Life's A Happy Song reprise (finale) ) In total: 11 song and dance numbers (12 if you count We Built This City)
So, pretty much, The Muppets has the most musical numbers.