Yes, this can be normal. Unfortunately, no one goes around talking about it. Everyone just talks about the famous hot flash - which I never get but would way rather have.
There seems to be a "disconnect" among the hormones sometimes and the body is not told to stop the period.
This happened to me 11 months ago. I was just going along, minding my business and one night during a class I was taking, I just started having a menstrual flood. It was like the blood was just falling out of my body in great gushes. This started one of the most horrible times of my life, with a period that went 17 days with great, gushing horrible clots and bleeding for days and days. By about the second week, I became very anemic from the blood loss but didn't know it. My skin looked jaundiced, I had pounding pulse and ringing in my ears and no strength. I finally realized and got sent to the ER (that experience was a joke) and eventually ended up being told to take 325 mg Ferrous Sulfate (65 mg elemental iron) 3 times a day. That gradually addressed the anemia and the period gradually stopped. I had another heavy period the next month, but of normal duration. Then from about April through August, I was happy to have normal, on-schedule periods. Then I went without a period during September, October and November. Then on Dec 3, 2012, it hit me again with a holy vengeance. 15 days of holy hell bleeding and clotting. I was more ready with the iron this time, but still, by the end I was weak and depleted. Period officially stopped but I did have some mild spotting during the next three weeks. I was so glad for those three weeks. Then on January 7, 2013, it hit me again. Normal period during that day and then the menstrual flood for about 2 hours starting at about 1:00 in the morning, and now I'm on the 12th day of a horribly heavy, clotty period. I so miss the summer when it had gone back to normal.
The thing is, there isn't enough said about this. There are many, many women who suffer with this and don't know about it and it is so panic-inducing!
I've read a bit on Susun Weed's website that this can be normal for YOU. I've hated the feeling of being blind-sided and terrified by it.