CES production function with non constant returns to scale
Another possibility is
\begin{equation}
Y=\left[ aK^{\mu_K\frac{\sigma -1}{\sigma }}+\left( 1-a\right) L^{\mu_L \frac{\sigma -1%
}{\sigma }}\right] ^{\frac{ \sigma }{\sigma -1}},
\end{equation}
with $\mu_K+\mu_L \neq 1$.
Edit: The function is not homothetic in $(K,L)$, and as mentioned by Giskard, the elasticity of substitution is not longer constant, unless $\mu_K=\mu_L$, in which case we obtain the specification proposed by cel.