Precision 7730. Three ports only run two monitors.

I bought a second hand Precision 7730. It has 3 video outlets.
HDMI, miniDP, and USB-C  as well as its own screen.

I wanted to run 3 external monitors, but I can only run 2. With the USB-C not connected, the monitor on the DP works, but with the USB-C -> HDMI cable, that monitor works, but not the monitor on the DP.

xrandr reports:
  eDP-1 connected primary 1920x1080+3840+0        so that's the laptop's screen
  DP-1 disconnected                               don't know what this refers to.
  DP-2 connected 1920x1080+1920+0                 Next to left hand monitor.
  HDMI-1 disconnected                             no idea why - one of the running monitors is via HDMI cable on the HDMI port
  DP-3 connected 1920x1080+0+0                    Left hand monitor. this monitor is connected via HDMI port on lappy to HDMI port on the monitor.

=============Ports to monitors====================
lappy ports                                   Monitors
HDMI                                          HDMI
miniDP                                        DP
USB-C          adaptor                        HDMI

============monitors working=========================
Monitor           Monitor                  Monitor            Lappy screen
working           working                  not working        working
HDMI - HDMI       USB-C to HDMI            MiniDP - DP

                                           But if the USB-C
                                           is pulled out,
                                           the DP monitor comes
                                           to life.

And by the way, turning off the lappy screen does not give me 3 monitors.

================inxi reports==========================
 garry@garry-Precision-7730:~$ inxi -G
 Graphics:
   Device-1: Intel CoffeeLake-H GT2 [UHD Graphics 630] driver: i915 v: kernel
   Device-2: Realtek Integrated Webcam_HD type: USB driver: uvcvideo
   ;    unloaded: fbdev,vesa gpu: i915 resolution: 1: 1920x1080~60Hz
     2: 1920x1080~60Hz 3: 1920x1080~60Hz
   OpenGL: renderer: Mesa Intel UHD Graphics 630 (CFL GT2)
     v: 4.6 Mesa 23.0.4-0ubuntu1~22.04.1

So it's looking like the lappy was not designed to run external 3 monitors.

It hasn't got NVIDIA or AMD discrete graphics , which seem to be better, but mine is Intel.

Next thought - can I use a dock, or maybe daisy chain DP, to run 3 external screens.

I think relevant specs are
https://dl.dell.com/content/manual43385134-dell-precision-7730-setup-and-specifications-guide.pdf?language=en-us

Table 14. Ports and connectors
Features Specifications
  ...
Docking port    -Cable dock support
Video           -Mini DisplayPort 1.4
                - HDMI 2.0
NOTE: For the systems with DisplayPort 1.4 HBR3
is applicable, and HBR2 for every system that has
DisplayPort 1.2.
Thunderbolt Two thunderbolt 3 Type-C ports

I'm just a bit wary of docks, because they seem to need such complicated support, and lots of people report disasters.