Looking on the internet deeply has found these results:

John and I jump is the most popular phrase on the web.

John and me jump 10 results on the web	John and I jump 173 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Feb 1, 2015 ... They do not respond so John and I jump in and switch to channel 68. They advise that the winds off shore are much stronger than anticipated�... Nov 20, 2014 ... Ben does the same and John and I jump into the car and follow them. After two km on the main highway, we branch off the tarmac towards Iltilal�... Dec 7, 2014 ... While watching the waders in the harbour, there was an almighty crack of gunshot, which made both John and I jump! Our attention then turned�... John and I jump on the Tube and head for Chelsea Harbour. We love the London Underground�it's so clean and the staff so helpful, unlike NYC. Time to Tweak!

John and me jump

10 results on the web

John and I jump

173 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Feb 1, 2015 ... They do not respond so John and I jump in and switch to channel 68. They advise that the winds off shore are much stronger than anticipated�...
Nov 20, 2014 ... Ben does the same and John and I jump into the car and follow them. After two km on the main highway, we branch off the tarmac towards Iltilal�...
Dec 7, 2014 ... While watching the waders in the harbour, there was an almighty crack of gunshot, which made both John and I jump! Our attention then turned�...
John and I jump on the Tube and head for Chelsea Harbour. We love the London Underground�it's so clean and the staff so helpful, unlike NYC. Time to Tweak!