Example of a (not quasi-linear) production function whose inputs are not perfect substitutes but are not asymptotic at the axes
You could, for example take the function $f: \mathbb{R}^2_+ \times[0,1] \to \mathbb{R}$.
$$
f(L,K, \rho) = L + K + (1-\rho) L K.
$$
For $\rho = 1$, we have $f(L, K, 0) = L + K$ which is a production function with perfect substitutes.
The marginal product (of say $L$) is given by:
$$
\frac{\partial f(L, K, \rho)}{\partial x} = 1 + (1-\rho)K,
$$
which equals $1$ if $\rho = 1$.