Paul Benne Specially Adaptive Housing Improvement Act of 2019 This bill revises the Department of Veterans Affairs (VA) Specially Adapted Housing Program, which provides grants to veterans and service members with certain service-connected disabilities to assist with constructing, purchasing, or remodeling homes to fit their needs. The program is comprised of two grants: the Specially Adapted Housing grant (for acquisition of housing with special features), and the Special Housing Adaptation grant (for adaptations to a veteran's residence). Specifically, the bill establishes grant priority for seriously ill veterans and directs the VA to define such term. The bill raises the cap on grants that may be issued per veteran from three to six and raises the number of applications that may be approved for the Specially Adapted Housing grant from 30 to 120. The bill increases the maximum amount of assistance available under the Special Housing Adaptation grant and also increases the aggregate amount of assistance available under both grant programs. The bill also authorizes certain veterans to apply for additional assistance under both grants, subject to specified limitations.