What are the limitations of the Ebers-Moll model of the BJT
The original Ebers-Moll model can't capture the Early Effect or any charge storage effects. It can be modified to include these: Mathworks NPN enhanced Ebers-Moll model.

There is also the Gummel-Poon model. It is possible to exactly get the Ebers-Moll model from the Gummel-Poon model by setting certain parameters to a certain value.

According to this derivation, Gummel-Poon is able to capture space-charge layer generation/recombination, as well as high-level injection (variation of \$\beta\$ with current?) and the Early effect. I didn't thoroughly look through the differences between the "enhanced Ebers-Moll" and the Gummel-Poon model.