How does getting 2 or 3 shots of the Pfizer or Moderna COVID vaccine compare against 1 shot Johnson & Johnson's vaccine + 1 shot of Pfizer or Moderna?

Question

I wonder how does getting 2 or 3 shots of the Pfizer or Moderna COVID vaccine compare against 1 shot Johnson & Johnson's vaccine + 1 or 2 shots of Pfizer or Moderna, in terms of COVID-19 protection. I'm mostly interested in the COVID-19 delta variant.

I couldn't find anything on it on Google. My findings:

• Israeli survey finds 3rd Pfizer vaccine dose has similar or fewer side effects.
• https://www.nytimes.com/2021/07/20/health/coronavirus-johnson-vaccine-delta.html: "The Delta variant is the most contagious version yet of the coronavirus. It accounts for 83 percent of infections in the United States"
• https://www.reuters.com/business/healthcare-pharmaceuticals/booster-may-be-needed-jj-shot-delta-variant-spreads-some-experts-already-taking-2021-06-25/: "Both mRNA vaccines showed efficacy rates around 95% in large U.S. trials, while J&J's vaccine was 66% effective in preventing moderate-to-severe COVID-19 globally when more contagious variants were circulating."

Answer 1

The Astra Zeneca vaccine which is similar to Johnson & Johnson's, was studied in combination with Pfizer's; they found using Pfizer as the second dose after a first dose of AZ gave better results than two doses of AZ: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3874014 "Safety and Immunogenicity Report from the Com-COV Study – a Single-Blind Randomised Non-Inferiority Trial Comparing Heterologous And Homologous Prime-Boost Schedules with An Adenoviral Vectored and mRNA COVID-19 Vaccine"