Augmented Gravity Model

I am currently using the gravity model for my dissertation on migration flows. Do gravity models need to be augmented by dummy variables only or can other explanatory variables (such as the unemployment rate in the destination/ origin country) be included please?

All your feedback is greatly appreciated.

\begin{align*} M_{ij} = &\beta_0 \times log(g) + \beta_1 \times log(P_i) + \beta_2 \times log(P_j) + \beta_3 \times log(X_i) + \\ &\beta_4 \times log(X_j) + \beta_5 \times log(D_{ij}) + \varepsilon_{ij} \end{align*}
where $$X_i$$ is a vector of explanatory variables describing different features of the origin (i.e. push factors) and $$X_j$$ is a vector of explanatory variables describing features of the destination (i.e. pull factors). Push factors are those characteristics of the origin place that encourage (discourage) out-migration (in-migration), such as low incomes, high unemployment, high prices, in general few opportunities for development.