Memantine
I don't know of anyone in our neck of the woods who prescribes it privately, but part of that is 'cause there's more to it than the prescription.
Firstly, the side effects need looking at, so there would need to be follow up to check out if there's any of the recognised problems of dizziness, confusion, headache, hallucinations, tiredness, vomiting, anxiety, hypertonia, cystitis and increased libido.
This would mean, after starting a private prescription, that there'd need to be a consultation to check out that the memantine's alright and isn't causing these difficulties.
Second hassle is the dose. It is anywhere from 5mg to 20mg a day, so needs to be increased over time in 5mg steps.
And, as well as seeing the person and checking safety and issuing a prescription, there's then the need, yet again, to review things to check out side effects.
So typically could be 4 consultations to get the dose right, and 4 consultations soon after each dose increase to check out side effects.
Thirdly, when on the right dose, there has to be monitoring of this. In part this is 'cause the dose of the drug can need to change as time ticks by, but in part it's also through dementia having different phases, so treatment (including drugs) might be right at one point in time but need fiddling with further down the road.
With this minimum input, that could be 9 reviews in the first year, with more necessary following up of things in subsequent months and years.
Bottom line is, if done right, there'd be a heap more to it than just getting a prescription a couple times a year!