Tagalys scores are based on historical data, that is considered to predict future behaviour. But say there is an external event, like a brand promotion, and products from that brand may not show in the first 4 pages of search results due to past data, you can chose the Search Merchandising tool, to influence visitor engagement by controling what your visitors see for a particular search query. 

Note: By merchandising a search, you are essentially altering the results recommended by Tagalys algorithm.