Yes you can do a Reg D offering concurrently with a Reg CF offering. However, you'd want to make the Reg D a 506(c), which permits general solicitation, because while concurrent offerings under Reg CF and 506(b) are theoretically possible, it can get very complicated, especially because in the CF you are going to have to disclose the existence of the Reg D offering (and vice versa).
What, if anything, do the regulations say about deal terms of concurrent Reg D and Reg CF offerings?
e.g. Can an issuer offer a different (cheaper) price per share to Reg D investors, offer warrants, different voting rights, or other "benefits" to incentivize them for writing larger checks than the ongoing Reg CF investors are getting?