all the more vs alternately

all the more

adv
  • Even more; notably, but even more notably due to additional information, either preceding or following the statement. 

alternately

adv
  • By alternation; when, in a proportion, the antecedent term is compared with antecedent, and consequent. 

  • In reciprocal succession; succeeding by turns; in alternate order. 

  • Alternatively. 

How often have the words all the more and alternately occurred in a corpus of books? (source: Google Ngram Viewer )