Dell laptop with at least 3 USB Controllers?

Are you actually asking about "Ports" and not "controllers"?  I don't know of any laptop (any brand) with 3 USB controllers.  

The Vostro 7590 has 2 USB 3.1 ports and 1 Thunderbolt port.  

I agree with @fireberd .  Some laptops will have two, but one of them might be dedicated purely to running internal devices that use USB, such as the keyboard, touchpad, touchscreen, webcam, Bluetooth module, etc. (WiFi+BT combo cards run WiFi over PCIe and Bluetooth over USB since mPCIe and M.2 slots support both).

I don't think you'll find a laptop with its chassis USB ports split across 3 USB controllers.  Are you trying to run an Oculus Rift where they recommend having each sensor on a dedicated controller?

Actually I would like to replace a Dell Latitude E5530, that has 3 USB controllers:

I need them to drive multiple lab equipments (debuggers, boards, etc.) that need a lot of endpoints. I have to avoid the Windows error message "Not enough USB controller resources".

Yes, I know how to use google

I would just like to know if a Dell laptop with 3 USB controllers (like the Latitide E5500) exists today.

https://helpdeskgeek.com/help-desk/how-to-fix-not-enough-usb-controller-resources-on-windows-10/

@gs71  Uploaded images are initially visible only to the person who uploaded them and to Dell moderators until they get approved for public viewing, but I'll check back and see what your E5530 looks like.  On my own Latitude 7480 with no external peripherals attached, my Device Manager's "Universal Serial Bus Controllers" section includes:

Intel USB 3.0 xHCI Host Controller
USB Composite Device
USB Root Hub

Only that top item is an actual controller, even though all of those devices appear in a Device Manager category called "USB Controllers".  Curious to see what your system looks like when the image comes through.

@gs71  Well your upload came through.  So it appears you have one USB 2.0 controller (EHCI) dedicated to running your device's internal components, such as Bluetooth, the webcam, and what appears to be a fingerprint reader.  Then your external ports are split between a USB 2.0 controller (EHCI) and a USB 3.0 controller (xHCI).  Does your system have a mixture of USB 2.0 and 3.0 ports?  If not, I think some early USB 3.0 systems retained EHCI controllers for when USB 2.0 devices were plugged into their USB 3.0 ports.  But it seems at least some other systems these days, like my Latitude 7480, run USB 2.0 through an xHCI controller, like the only one in my system.

In any case, I don't know of any systems with multiple USB controllers built in, although in fairness that's not exactly something I check when I use various PCs, nor is it something you'd ever see in published specs.