Not really, but I did recently try mine; which in theory is a Hitag, but I struggled even getting a read on my Proxmark.
Do you by chance have a VW or AUDI?
The more likely option rather than a NExT would be an xHT HITAG S2048 Chip from Dangerous Things
I don’t think you can “easily” copy it to then write to the xHT, in THEORY you may be able to enroll it, but I don’t know enough about them to confirm that.
For what I wanted to do, it was faster and easier to remove the chip from my key and mounting it over the antenna coil on the ignition barrel.
Alternatively you could use the same thing @darthdomo used in his CaRFID project
THEN use your NExT to do your unlocking / starting of your car.
We can give you some suggestions if you need them.
I regret not pursuing the writing / enrolling / copying / cloning of my Car immobiliser chip, but I only had one chip and after research I found out the chip can be “bricked” during the READ although unlikely ( I got this information from the guy with the “special” writing tool )
I have 2 blank chips that I removed from my spare keys I had cut, I believe these to be HiTags, but can’t confirm until I get a read, but still struggling with the PM3.
The cost for the guy to copy to my blank tags was more than buying my own reader / writer off Aliexpress.
Something like this
My bypass worked out for me to be much faster,so this is a low priority amongst my many projects.
Further research is still required on my end.
If I buy a reader/ writer and have some success, I will keep you in mind and I can send it out to you. ( I am not planning on this in the near future )
Likewise, Please update your thread if you have any success 
No a great answer for you, but I hope it is of some help!