Remember that all internships last 12 weeks. This may sound silly, but you should actually count out the weeks when establishing starting and ending dates - May 19 to August 19 is not 12 weeks!!
Interns are hired on a rolling basis: each week several agencies conduct interviews, select and hire an intern. The two or three applicants not selected by an agency go back into the pool and may be interviewed for another project with another agency. Interns may be interviewed for several projects but will only be offered one position; by declining one position, one declines to participate in the program at all.
If a sponsor contacts you, please work with them to set up an interview time immediately. If a sponsor cannot get in touch with an applicant quickly, that applicant will no longer be considered for that position.