I assume you're refering to the latest version UltraEdit. This is not possible, even in UE 14.20 RC1. However multiline file tabs are available in UEStudio 6.x, along with the option to have the tabs at the top or bottom of the screen.
Sorry Frank, but your answer is not correct. Also UltraEdit supports multi-line file tabs and also UltraEdit supports the file tabs docked at top or bottom of the main window or floating.
For multi-line file tabs in UltraEdit you just have to increase the file tab area as you can see on the following screenshots.
Move the mouse over the divider line between the file tabs and the edit window and click and hold left mouse button.
Drag down the line to increase the file tabs area.
Increased file tabs area with multiple lines.
Best regards from an UC/UE/UES for Windows user from Austria