Test Homogenity of Regression slopes for a one-way ANCOVA with two covariates

Hello everybody, I am working with R for the ancova analysis now. As far as I understand, to test the homogenity of regression slopes in Ancova, we have to check for the interaction between the Group*Covariate, but that only works if we have one covariate. How to test the interaction when there are 2 covariates, is it the same like with one covariate??

which gonna look like this in R:

model <- lm(dep ~ group + cov1  + cov2 + group*cov1 + group*cov2)
Anova (model, type="III") 

Is it actually the right way to do it? I can not really find any documentation about dealing with homogenity of slopes for multiple covariates. Thank you for your help!

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