With or without the Dawnguard DLC, you can't (without the use of PC-only console commands) switch back and forth as many times as you would like between being a werewolf and being a vampire.
According to the UESP wiki's "Aela the Huntress" article (emphasis mine):
If you have cured yourself of lycanthropy, there is no way to regain it in the base game. However, the Dawnguard add-on provides a one-time opportunity to restore your lycanthropy by speaking to Aela.
After being cured of lycanthropy, simply find Aela and speak with her. You will have the option to tell her you wish to regain the gift of beast blood. She will respond, "Do you, now? Hircine doesn't usually bestow his favor on the fickle. But you've proven your worth. I'm willing to try. Are you ready now?" If you tell her you need more time to prepare yourself, she will end the conversation by answering, "Go. Reconsider your plight." If you then return to her you can go through the conversation again, and it will continue as before. When you choose to tell her you are ready, she simply says "Hold still, then." Your screen will turn black for a second, then a magical aura will circle around you and a message will appear on the top left of your screen stating "Beast Blood Added". The conversation is now over, and if you choose to cure your lycanthropy again, there will not be another chance for Aela to restore it.
TLDR: Without the Dawnguard DLC, you can only become a werewolf once. With the Dawnguard DLC, you can become a werewolf twice, if you've cured yourself of lycanthropy the first time around.
If you are playing on the PC and have the Dawnguard DLC installed, you can use console commands that will allow Aela to turn you into a werewolf after your second time to be turned (allowing you to easily switch to being a vampire and werewolf back and forth as many times as you would like). You can do this by entering the console commands then conversing with Aela to turn you into a werewolf, and conversing with Serana to turn you into a Vampire Lord (or just be a vanilla vampire).
You can enable the conversation option "I wish to regain the gift of beast blood" to Aela with the console command:
If you encounter issues with the above console command, enter
player.setstage F6090 100 to force a cure before using the console command to enable the conversation option.
Console commands info from: The Nexus forums post, "Dawnguard Regifting Lycanthropy "
Serana won't be able to turn you into a Vampire Lord if she has cured herself of vampirism.