@Mrs.Tibbs6972 There are several things you need to consider before you start to look for a desktop:

1. What type of inputs (HDMI, DisplayPort, DVI, etc.) do your existing monitors have?

2. Are you running your monitors at a high resolution (i.e. 4K) and high refresh rate (120 Hz or higher) or are you running standard 1080p at 60 Hz?

3. If you are running three monitors I would strongly suggest a desktop with a discrete graphics cards. Most newer discrete graphics cards that come with Dell desktops have only DisplayPort and HDMI output ports but some may have DVI ports, but in most, but not all cases you will unlikely find three ports of the same type, usually, it is a combination of DisplayPort and HDMI (usually more DisplayPort than HDMI), so don't rule out the need for some sort of adapter (i.e. DisplayPort to HDMI). 

4. If your monitors don't require high refresh rates or resolutions you may be able to use a USB-C to multi-monitor adapter or a DisplayPort to multi-monitor adapter. Have you considered using something like that with your HP All-In-One? If your HP meets your other needs then maybe a multi-monitor adapter is your solution.

5. Is three monitor support your only consideration for a new desktop? Since you mentioned working from home I assume you are not playing games, but does your work impose any other special requirements on your desktop?

@Mrs.Tibbs6972   - What about just getting a USB3>video adapter for your current PC to connect the 3rd monitor?  Where "video adapter" is a type of port your 3rd monitor supports, eg HDMI or DisplayPort (DP).

Make sure the USB3 adapter supports your version of Windows and the "native" (aka: recommended) resolution for the monitor connected to it.

A reasonable USB3>HDMI adapter may only cost ~$20-$30. A USB3>DisplayPort adapter may cost more.

I don't want to hijack the thread, so please pardon me, and if this is inappopriate please direct me elsewhere! -- but I recently counseled a forum user that since they don't have Thunderbolt or USB-C alt mode on their Optiplex 7090 SFF systems, they'll need a discrete video card to get three monitors connected. I'm obviously all wet, but you'll grant me that it's confusing. Apparently some of the cheaper USB3-to-video adapters are garbage -- par for the course -- but they all seem to come from these little companies with unpronounceable names. Is there something a user should look for in one of these adapters to ensure they're getting a decent one? Is there a real difference in how the Thunderbolt and alt mode adapters work (for video, not the other stuff) vs. these? (I'm directing my unfortunate counselee here, by the way.) Thanks...

@RoHe , thanks! -- I'm also seeing recommendations in some of the Amazon reviews for adapters that use Synaptics' DisplayLink technology and drivers. , e.g. this one. Those seem to skew a bit more expensive but perhaps are more dependable. Complaints about the cheaper ones include dodgy drivers, performance hiccups in video and/or other USB devices, and excessive heat in operation.

@NJDave  - There are a number of important issues/questions here...

• USB2 vs UBS3: USB3 has more bandwidth so performance should be better than USB2
• Intended use: gaming, streaming video or just routine office work?
• Monitor's "recommended" resolution: adapter must support that resolution
• Size of monitor: USB>video adapter performance tends to decline the bigger the monitor
• System RAM: More is better
• Cost1: cheaper than new PC, or new add-in GPU
• Cost2: Higher price may -or not- mean better performance
• There are adapters from well-known companies
• Read professional reviews of USB video adapters