Per the guidance materials, no (see below). However....if the institution has multiple campuses with different DUNS numbers, they can.
A grantee under the HSI program, which is authorized under title V of the HEA, may not receive a grant under any HEA, title III, part A program. The title III, part A programs are: SIP; the Tribally Controlled Colleges and Universities program;
the Alaska Native and Native Hawaiian-Serving Institutions program; the Asian American and Native American Pacific Islander-Serving Institutions program; and the Native American-Serving Nontribal Institutions program. Furthermore, a current HSI program
grantee may not give up its HSI grant to receive a grant under SIP or any title III, Part A program as described in 34 CFR
607.2(g)(1).