Searching multiple booking calanders

Is the following possible,  even using an  API solution

We have different people who have a booking calander.   Each of these people offer a Service at a certain location and at a certain cost.

We would like to be able too allow customers to  enter a search field in our website, built on what ever stack,  and  they would then get a link to a booking page that meets their criteira,  

say finding someone who does X ,  on X date  at X time.