Can I combine a dplyr mutate_at & mutate_if statement?

Unfortunately the solution of @kath onyl works in given example but fails if only one column contains data, eg:

country country-year year     a     b
France  France2000   2000       NA    NA 
France  France2001   2001     1000  1000  
France  France2002   2002       NA    NA
France  France2003   2003     1600  2200
France  France2004   2004       NA    NA
UK          UK2000   2000     1000  1000  
UK          UK2001   2001       NA    NA
UK          UK2002   2002     1000  1000  
UK          UK2003   2003       NA    NA
UK          UK2004   2004       NA    NA
Germany     UK2000   2000       NA    NA 
Germany     UK2001   2001       NA   500
Germany     UK2002   2002       NA    NA  
Germany     UK2003   2003       NA  1100
Germany     UK2004   2004       NA    NA

Unfortunately too, the answer to the OPs question is no, you can't mix mutate_at and mutate_if (there's no function that allows you to specify .predicate and .vars)

but you can use a predict function within the function used in mutate_at. So here is my solution using mutate_at containing a predict function:

df %>%
  group_by(country) %>%
  # Interpolate if at least two non-null values are present
  mutate_at(vars(a,b), funs(if(sum(!is.na(.))<2) {NA_real_} else{approx(year, ., year)$y})) %>% 
  # keep only rows with original or interpolated values in either column a or b
  filter_at(vars(a,b), any_vars(!is.na(.)))