The internet loves parallel projects.
Linux development is parallel. Thousands of people can work on it at once, none of them waiting in line. Wikipedia is parallel, because a large group can go at millions of articles, side by side. The YouTube Orchestra auditions were parallel too, because you didn't have to wait in line to practice or apply.
Parallel is faster and more efficient. The Huffington Post will always outperform a traditional news site because they have 3,000 contributors, not a few dozen.
If you want to make a buffet go faster, all you need to do is move the serving table away from the wall and let people serve themselves from either side. If you want to go faster still, use two tables.
Self-service customer support outperforms the traditional model because people don't have to wait in line.
Your organization probably isn't parallel. There are bottlenecks throughout, and finding them and making them parallel could change everything.
There's one place you don't want to be parallel, at least at first: sales.
When you are linear in your sales process, you learn something. You don't make the same mistake on each and every call. Instead, you make a few mistakes on your first call, then a few less and then, finally, you get it as right as you're going to get it. That is when you go parallel, not before.