It's been two months since the "Fusion Wave" hit your city. You were just sitting down to dinner with your mom and dad when it happened. Just as you were starting to take a bite of the meal your mom had made, a wave of extreme heat passed through the house and you all blacked out.
The next moments you remember were extremely confusing. As you woke up, you realized you were seeing out of three pairs of eyes. After a few moments of blinking to make sure you weren't seeing things, you looked to your sides and saw, from different perspectives, that both your mom and dad's heads were now on either side of yours on the same pair of shoulders, though, their faces seemed to be a bit younger than before. Looking down, you realized that the Fusion Wave had done a number on your family, merging both your parents and you into one. Your new body, which was now naked due to the fusion, looked like a combination of the three of you: A slightly muscular frame but with soft feminine skin, C-cup breasts, and both a penis and vagina sitting between your legs. Your combined body now looked in its late 20's along with your heads, with you aging up and your parents aging down.
After a moment of freaking out more, you began to realize that your parents heads were now under your control. It seemed that the wave merged all three of your minds into one, but kept yours as the dominant one in control. You could access both your mom and dad's memories and could speak with each individual head, though it required a bit of concentration. The more comfortable thing to do was speak with all three heads simultaneously. It was so weird hearing your mom and dad speak in perfect synchronicity with you, but over time you got used to it.
The last few months have been an extremely hard adjustment period. Considering your physical and mental fusion was extremely rare, even by the standards of the Fusion Wave, there was an extreme learning curve to your new life.
Despite being a full fusion, you decided to try and keep up appearances of being a physically fused family, rather than a mental one as well. You continued to go to work at your dad's job, had brunch dates with your mom's friends (who had also changed), and had other friends over to your house to hang out. Due to your combined minds, you could feign you and your parents individuality and no one was the wiser.
As you woke up on Saturday morning marking the second month since the merger, you opened all six eyes and decided what you would do today.