Advanced search with custom fields

I have added several custom fields to the Places post type (see attachment1.png). I want one select box to show in the main search that will provide a list of all of these custom fields. For example say I’ve created the following custom fields as checkboxes:
Custom Checkbox 1
Custom Checkbox 2
Custom Checkbox 3.
Now, in the main search on the front page (see attachment2.png) I want a select drop-down input that when clicked will allow the user to select one or more of these custom fields and then of course only return Places that have these custom fields checked. I am aware that I can conceivably accomplish this with the multi-select custom field however that shows only in the advanced search area, not in the main search box.

I have searched through the advanced search forum for a resolution for this and I cannot find any.
Any help would be much appreciated.