Simon has recently done a substantial SoPD blog post on this (and related) research:

From Alchemy to Alkahest | The Science of Parkinson's

From Simon's SoPD blog post, here is my understanding of the current state-of-play regarding "young plasma for PD".

The clinical trial that Nan_Cyclist took part in (NCT02968433), conducted at the Stanford Movement Disorders Clinic, is now coming to an end.

Independently of this, researchers (from Stanford University and Alkahest) who conducted the earlier "young plasma for AD" trial (NCT02256306), have "distilled" young plasma into an injectable "drug" (GRF6021) that is now being tested in a Phase 2 trial involving 90 volunteers with either PD or PD with mild cognitive impairment (NCT03713957).

An earlier version of the drug (GRF6019), consisting of about 400 proteins, is currently being tested on volunteers with either mild-to-moderate (NCT03520998 ) or severe (NCT03765762) Alzheimer's disease.

For anyone who might be interested, the new PD trial is currently recruiting PwPs.

A Study to Assess the Safety of GRF621 Infusions in Subjects With Parkinson's Disease and Cognitive Impairment - Full Text View - ClinicalTrials.gov

I've come across some PD pre-clinical research with mice, using cord blood plasma (CBP). Possible future plans include combining CBP with mesenchymal stem cells.

Gutting the brain of inflammation: A key role of gut microbiome in human umbilical cord blood plasma therapy in Parkinson's disease model. - PubMed - NCBI

Here is my understanding of the current state-of-play regarding "young plasma for PD" clinical trials.
​
​The "young plasma for PD" trial that Nan_Cyclist took part in (NCT02968433), conducted at the Stanford Movement Disorders Clinic, is now overdue for completion.​
Status: Active, not recruiting
Estimated Study Completion Date: December 2019 (no results published AFAIK)
​
​Independently of this, researchers (from Stanford University and Alkahest) who conducted the earlier "young plasma for AD" trial (NCT02256306), have "distilled" young plasma into an injectable "drug" (GRF6021) that is now being tested in a Phase 2 trial involving 90 volunteers with either PD or PD with mild cognitive impairment (NCT03713957).​
Status: Active, not recruiting
Estimated Study Completion Date: November 2020
​
​An earlier version of the drug (GRF6019), consisting of about 400 proteins, was tested on volunteers with either mild-to-moderate (NCT03520998 ) or severe (NCT03765762) Alzheimer's disease.​
Status (of both): Completed
Results: In December 2019, Alkahest presented data from NCT03520998.

Alkahest Presents Data from Phase 2a Study in Mild-to-Moderate Alzheimer’s Disease:
Alkahest Presents Data from Phase 2a Study in Mild-to-Moderate Alzheimer’s Disease - Alkahest

In addition, Alkahest have recently started a trial "Assessing Efficacy and Safety of AKST4290 in Subjects With Parkinson's Disease on Stable Dopaminergic Treatment". AKST4290 (a non-plasma-derived product) is an orally-administered small molecule that acts as a modulator of inflammation. More information on AKST4290 (formerly called ALK4290) is available in this SoPD blog post from Simon (December 2018):
From Alchemy to Alkahest | The Science of Parkinson's

For anyone who might be interested, the new PD trial is currently recruiting PwPs.
Study Assessing Efficacy and Safety of AKST429 in Subjects With Parkinson's Disease on Stable Dopaminergic Treatment - Full Text View - ClinicalTrials.gov

The "young plasma for PD" trial that Nan Cyclist took part in (NCT02968433), conducted at the Stanford Movement Disorders Clinic, has published its results.

PNT Article - Young Plasma Infusions Safe and Potentially Helpful, Small Trial Finds:
Young Plasma Safe and Potentially Helpful in Parkinson's, Trial Finds.

See also this SoPD blog post from Simon:
The Stanford Parkinson's Disease Plasma Study - The Science of Parkinson's