Counting the number of rows for different combinations of factors

Considering a dataset such as the classical mtcars, I want to know the number of observations (=rows) by different levels of factors, taking them separately as well as together.

For example, the following code will generate a column N with the number of observations per level of cyl and gear, but not the number of observations for cyl and gear separately.

mtcars %>% dplyr::group_by(cyl, gear) %>% dplyr::summarise(N = n()) 

I know that a separate number of observations for cyl and gear can be obtained just in a similar way, creating separate dataframes, and merging all together. The following would generate the expected output:

df <- mtcars %>% dplyr::group_by(cyl, gear) %>% dplyr::summarise(N = n())
df_gear <- mtcars %>% dplyr::group_by(gear) %>% dplyr::summarise(Ngear = n())
df_cyl <- mtcars %>% dplyr::group_by(cyl) %>% dplyr::summarise(Ncyl = n())
df %>% dplyr::left_join(df_cyl) %>% dplyr::left_join(df_gear)

But I am wondering if there is a cleaner way to generate this dataset, hopefully without needing to generate intermediate datasets.