Cartridge (other than Rega) with Rega RP10

I have been using a Lyra Kleos on mine since day one. In advice from Jonathan Carr (Cart designer) I was able to acquire shims for 3.5mm  at the base of the tonearm. Mr Carr recommended 3.4mm but unless I have shims specially machined, which I may do someday, I figured .1 mm can’t be that crucial with varying LP thickness. 
Something to ponder should you decide on Lyra, I think they are all the same height. But I do find the Rega and Lyra work well together when set up correctly.  Years ago I had a Rega P25 and used a Benz Glider and traded to a Lyra LydianB and found the Lyra much more pleasing.
Good Luck

Ladok, sorry especially one responding earlier. But yes, I consider the Lyra as a house sound. I find they have a delicate revealing sound with over analyzing. Top to bottom I find them to deliver what is ever in the groove. To a point that I have experimented with adjustments and find that extraction increases as if the cartridge can read it, if the tonearm settings and cartridge alignment are correct. That said, I am sure this is with any cartridge, the full potential of a good cartridge is dependent on set up. Like the best tire can’t fully perform with bad alignment and suspension. 
As far as the Lyra House Sound, you need to experience it to know if you will love it. Is there a Rega dealer in your area that sells Lyra. See if he is willing to set one up for you. Regardless of which cartridge he uses, you should get a feel for the sound Lyra brings to the table.