I made a Generation C# out of a C and a B out of a Bb. The same approach would work for making an E out of an Eb.
1) chop the tube at the top until the upper-hand notes are in tune in the new target key. Usually
xxx ooo
xxo ooo
xoo ooo
oxx ooo
will all be close together and shouldn't need any further adjustment.
Next chop the bottom until xxx xxx is in tune in the new target key. What you'll now find is that xxx xxo and xxx xoo are flat and these two holes will have to be carved out quite a bit. My Gen C# and B play great.
To go lower you have to add tubing. I made a Gen A out of a Bb by making a new body. It plays great too.
Here they all are, Generations in A, Bb, B, C, C#, D, Eb, and F. That Gen Bb was horrid and I have a terrific Freeman Gen Bb now.