In some cases the answer is yes. For instance, as of 2020, there is a pathway for "SBIR Direct Phase II" awards for NIH (one of the grant giving agencies). According to the NIH SBIR FAQ page in 2020:
As part of the SBIR and STTR Reauthorization of 2011, NIH may ‘issue a Phase II award to a small business concern that did not receive a Phase I award for that research/research & development'. This 'phase flexibility' is called a ‘Direct-to-Phase II’ SBIR award. This permits small businesses to receive a Phase II award even if they have not previously received a Phase I award for the research/research and development of their technology. In order to be eligible for the SBIR Direct Phase II award, the small business must have performed the Phase I stage-type of research through other funding sources.
The Direct-to-Phase II authority is not available to the STTR program and not available for the CDC, FDA, and ACL SBIR programs.
The prior program had specific SBIR Direct-to-Phase II funding opportunity announcements (FOAs). The transition to FORMS-E allows NIH to track SBIR Direct-to-Phase II applications at the Application level, as there is a new check-box on the SBIR/STTR Information Form for Direct Phase II.
As a result of this, NIH does not need to issue separate SBIR Direct-to-Phase II FOAs as before, but can offer Direct-to-Phase II as an allowable Application Type on any SBIR FOA. SBIR Direct-to-Phase II application are 'New' submissions and are not Renewals.
Applicants are strongly advised to discuss this option with their Program Officer well in advance of any due date.
This article builds on content developed by the Martin Trust Center for MIT Entrepreneurship for MIT's Orbit Knowledgebase and is licensed under CC BY-NC-SA 4.0.