Most likely Dan Aykroyd doesn't own the rights to the movie. I'm guessing Harold Ramis owned the rights and once he died, whoever retained the rights was free to have a field day with it. If he was alive I doubt it would include the current cast. Ramis had talked about a sequel for years.
If you want a good story about the way movie rights work and how the little guy sometimes wins in the end, check out what happened with Super Troopers. The original writers/actors, the comedy troupe Broken Lizard, made the deal for the original movie as an up and coming group. They didn't know it at the time, but they signed a terrible deal that gave the creative rights to the studio. If I remember correctly they didn't even have royalties on DVD sales. Seems insane now, but it came out in 2001, which is just when DVD was catching on. They probably signed the deal in 99 or 00 so DVD was in its infancy. The movie did fairly decent in the box office for an unknown comedy, but it fell more along the lines of cult classic as it got really popular when it came out on DVD. I was in college and EVERYONE owned a copy of that. People would quote from it daily.
So after the success, naturally the studio wanted to make a sequel a la Hangover II same plot, same characters, same jokes just a quick follow-up to make as much money as possible. Broken Lizard really wanted to do a sequel, but the right way and written by them. They had some other movies in the pipeline at that point, and had learned their lesson, so they could say no to the project. Even several years later when BL was ready to do a sequel they still didn't have the rights, so they would have had to do it under a different name with different characters, etc. So they waited. And waited.
This April, fourteen years after the original was made, the original team started a crowdfunding campaign for a sequel. Fox Searchlight agreed to release the movie if they could raise $2 million. They raised $5.7 million with over 50,000 donations made surpassing the 2 mil mark in 26 hours.
Now, we'll see if the sequel is any good, but at least if it isn't it was given the best shot by the people who came up with the original. I think the encouraging thing is that there is an alternative emerging to the Hollywood machine. The internet is giving the people more of a voice than just voting with their wallet at the box office.