How to add a third display ?

you can try add a small low profile short bracket video card such as Dell oem R5 340 quite inexpensive 10-12 USD wich should give you a third DP video port.

BIOS did not say if multi display is supported

https://www.dell.com/support/manuals/en-mk/inspiron-3020-small-desktop/insp_3020_sff_ss/back?guid=guid-f2dda353-ba5a-44c0-b85f-6bf1b8c70d15&lang=en-us

service manual

https://www.dell.com/support/home/en-us/product-support/product/inspiron-3020-small-desktop/docs

@redxps630​ Thanks -  I guess I'll have to try and see if I lose any on-board port.  At least I should get a native DVI rather.  I'd rather not lose the HDMI, though.

There's always a USB3>video dongle (with whichever type port you need) as an easy/inexpensive way to add a 3rd monitor.

Just make sure the dongle supports your version of Windows, and the recommended (AKA: "native" or "optimal") resolution of the monitor that will be connected to the dongle. 

@RoHe​ I've tried one of these (>VGA) which shows under Devices as a Fresco Logic FL2000 USB Display Adaptor.  Even though it wired to its own USB3 port the display keep flickering and even disappearing for a second or two. There doesn't appear to be a Windows11 driver for this. I could try a >DVI version but a used Dell Radeon graphics card from eBay will cost little more.  Is there anything I need to keep a lookout for / avoid? Either way, I'll also need to buy another DVI cable (the monitor takes VGA or DVI).

A Display Port splitter also appears to be an option but these are quite a bit more expensive and I would also need a further Display Port video adaptor.

Thanks for your suggestions, Ron.

@IanMK13​  - Odd that the monitor connected to the USB>VGA dongle flickers.  Which CPU and how much RAM is installed in this system? 

How much junk is running in the background?  Try disabling unnecessary stuff that loads at every boot, eg SupportAssist/Dell Update, etc.

If you want a (used) GPU, you need a "half height" PCI-e (Gen3) x16 card. Try  to get one with as much of its own RAM as possible. Also make sure it has some sort of warranty...

@thinkdigital495​ , thanks for your suggestions. 

As stated above, I’ve tried a USB3 solution but it was unusable; very unstable.  I’m trying to keep my existing basic monitors, so daisy chaining and MST options aren’t an option. I’ve used most of my budget on the new PC so I’ll try picking-up a used graphics card. From what I can see, they generally only have two ports so I’ll  have to and it will run alongside the built-in graphics ports. 

@RoHe​ It’s a new PC, less than a week old. Intel® Core™ i7-13700 (24 MB cache, 16 cores, 2.10 GHz to 5.10 GHz Turbo) with 16GB. I’ve removed most of the bundled software but not addressed the start-up programs - I’m still finding my way around Windows 11. I’ve been looking at something like https://www.ebay.co.uk/itm/184392548668

I'd look for a GPU with HDMI and DisplayPort outputs, assuming your 3rd monitor supports either of those ports, rather than DVI. 

DVI is getting old and not many monitors still support DVI.  From what I can see at the link you posted, that card is DVI (Dual Link), so if you really want DVI, confirm the port type on the card and that at least one of your monitors supports the same type of DVI.  Also confirm the card's DVI port supports the "recommended" resolution for your DVI monitor.

If it's the same as this Dell OEM card, it's only PCI-e x8. While it should fit and work in the x16 slot, it won't perform as well as an x16 card (assuming the x16 slot on the Inspiron motherboard is wired for 16 lanes).

FWIW, you don't have to buy a "Dell" OEM video card, especially one that old.  According to the Inspiron 3020s specs, the PSU is only 180W so that does put a serious limit on what cards will work. So be sure to check the "recommended" PSU size for any card before you buy.

Although I've spent many years with my existing display setup and have become very familiar with moving windows between them, I think I may now have to bite the bullet and replace my main two 17 inch monitors with one wide monitor.  At present, I like the way that I can maximise a window to fit a display with 1 click.  I know that I can place two windows side by side and fill a display but it's not quite the same.