Luggage on the Access Narita Bus

Hi everyone! My bf and I will be travelling with 2 large suitcase per person (alternatively 1 large and 1 medium sized suitcases per person) since we'll be staying in Tokyo for 5 weeks and also intend to buy quite some stuff.
The Access Narita bus (from Narita Airpot to Ginza Sta.) allows 1 suitcase per person as stated on their website. My question to you is: Do you think it would be possible for them to allow 2 pieces of luggage per person eventually (maybe at additional cost) or is this an absolute no-go from your experience? (We'd be taking the bus sometime between 11AM and 1PM, is there a chance of it being very crowded?)
Thank you very much for your input in advance :)

Use Airport Limousine Bus to Ginza. They will allow you to bring two suitcases each passenger.

I don't know if they allow more than one, since I only had one to begin with (I had sent another ahead of time to the airport).

I reserved ticket online through their website and showed them my reservation from my phone. I think I took the 7:30ish morning bus from Tokyo Station; it was completely filled up (save for my seat) and there was a queue waiting. I was glad to have booked that seat. May or may not be the case always.