Linear Multistep Method With No Spurious Fixed Points

Question

For a general linear multistep method, i.e. a method of the form

$\sum_{j=0}^s \alpha_j x_{n+j} = \triangle t \sum_{j=0}^s \beta_j f(x_{n+j})$

Is there any way to manipulate the coefficients $\alpha_j$ and $\beta_j$ in order to ensure that the method inherits all fixed points of the underlying ODE and no spurious ones?

Thanks