Does the OLS regression line pass through the mean of ALL covariates?

Question

So in a OLS simple linear regression, the regression line passes through mean of X and mean of Y. It also passes through the point (mean X, mean Y).

Is this still true for a OLS multivariable regression. Does that regression line pass through the mean of Y and all the Xis? Does it also pass through the points (mean Xis, mean Y).

Thanks!