Attachment if
Because the parts (if test-expression then-expression else-expression) an else if would have to insert the new if as else-expression :
 (if test-expression1 then-expression1 (if test-expression2 then-expression2 else-expression2)) 
Using cond
In other languages, else if usually at the same level. For lisps for this we have cond . Here is the same with cond :
 (cond (test-expression1 then-expression1) (test-expression2 then-expression2) (t else-expression2)) 
Note that the expression may be just that. Any expression, so often, is similar to (some-test-p some-variable) , and other expressions are usually the same. Very rarely, these are just single characters to evaluate, but it can be for very simple conventions.