Inspiron 3670, additional HDMI port

By saying purchase Dell's suggested card, if you meant adding video card with HDMI to your computer.  The answer is yes, you can add a video card to designated PCIe slot on motherboard.  These are the cards which have been tested and validated by Dell.

Most of those video cards can use power directly from the motherboard, certain card like the GTX 1060 will require external power connector to provide additional power.  If you intend to use such card, check your power supply to see if it already has the required video power connector.  Or you can just verify if you have a 365w power supply.  Below is the OEM power supply options for the Inspiron 3670.

You may also purchasing video from retail market.  Just verify the fitment and power requirements before making purchase.

buy something like a gt 710 or gt 1030 if you just need a few extra displays, depends what monitor and refresh rate you are trying to drive.

Or, there's always a USB3>HDMI dongle as an simple/inexpensive way to add a 2nd HDMI port.

Just make sure the dongle supports your version of Windows and the "recommended" (= "native" or "optimal") resolution of the monitor to be attached to the dongle.

If you want to install a "retail" video card, you should disable Secure Boot in BIOS setup first. Otherwise, PC may not boot.