How do I change the product count per page to 20 from 16 for Search & Merchandising pages?

Override the search template by copying

app/design/frontend/base/default/template/tagalys_search/index.phtml 

to

app/design/frontend/YOUR-PACKAGE/YOUR-THEME/template/tagalys_search/index.phtml 

and changing

$('#tagalys-namespace').tagalys_search_results();

to

$('#tagalys-namespace').tagalys_search_results({per_page:20});