The antenna has been designed and fabricated.
Here are the impedance on each band.
Band 1: 0.699 GHz - 0.960GHz, Impedance: 11.756 - j135.919
Band 2: 1.71GHz - 1.99GHz, Impedance: 231.817 + j229.845
Band 3: 2.11GHz - 2.17GHz , Impedance: 63.544 - j186.479
If antenna have been fabricated, why? It is in that case very poor fabricated antenna.
Impedance curve shows poor matching for all frequencies and measured values from above does not even seem likely that they are correct measured or else is it an unusual antenna.
I did use your values from above but added some smoothing so that it did become a curve instead of three dots.
Smoothing is relative small and follows your impedance values rather close.
Your untuned antenna impedance is plotted below as yellow curve.
As can be seen is it a strange looking impedance curve but I accept that this is a correct measured antenna impedance.
For decent impedance match should actual frequencies be within red circle, corresponding to VSWR less then 3:1.
This curve is way off.
It is correct that it is a very wide frequency range to tune. Result is often limited and good impedance match is not a guarantee for an effective antenna. This antenna curves do actually show signs that it is a non radiating resistor more then an antenna.
Just as an example for your antenna, as a proof of concept, yes it can be wide-band tuned to be acceptable impedance matched.
AnTune software did automatically select best topology and then selected optimal components. Result is as below.
VSWR before matching is orange curve and yellow curve is after matching. All your required frequency ranges have now a VSWR better then 3:1.
Matching network is a relative simple T network:
S-parameters used for calculations for the coils are from Murata LQW15. It is important to not change this type without recalculate the network, especially due the use of L2 68nH with self resonance frequency of 2.5 GHz, any else type or brand will behave rather differently.
C3 is sensitive for fringing losses, which may need adjustments to compensate for, depending om PCB layout.
Resulting values:
Orange - original unmatched.
Yellow - matched curve.
Have also attached a zipped file containing S-parameters for your assumed antenna impedance after that I had smoothed it a bit and final S11 with tuning network applied, in case you want to double check result.