Yes, you can. These programs have different purposes and are not mutually exclusive.
EIDL: Covers emergency operating expenses and economic injury caused by disasters.
PPP: Helps businesses maintain payroll and certain other expenses during the pandemic.
SBA 7(a): Provides financial assistance for a wide range of business purposes, including working capital, expansion, and equipment purchases.
When applying for an SBA 7(a) loan after receiving EIDL or PPP funding, emphasize your future growth plans and how the loan will be used to expand your business. Highlight your business's financial health and ability to repay the loan.