A few more I can think of as of now, but I'm sure I have a lot.

• Games People Play & Old and Wise by Allen Parsons Project
• Fountain of Sorrow by Jackson Browne
• Send In The Clowns by Judy Collins
• Vincent (Stary Stary Night) by Don McLean
• Lay Me Down by David Crosby and Graham Nash
• Variation of a Theme of Erik Satie by Blood Sweat and Tears
• Just Too Many People and Midnight Blue by Melissa Manchester

To Shortandcute, Rainy Day Feelin' was done by The Fortunes and I Wish It Would Rain was done by The Temptations and Phil Collins (though two completely different songs).