This is hypothetical, and it shouldn't happen to anyone... In the middle of observing shiva for one's mother, that person's father dies. Do the two shivas overlap, or does one wait for the first to end before starting the second?
If two family members die on the same day, only one shiva is observed. If a family member dies during shiva, shiva for the second relative begins concurrently with the first. There is no need to sit shiva twice consecutively.
For example, a person is observing the second day of shiva and hears that another relative has died (and was buried), he observes shiva 7 days starting from now, for a total of 8 days.
Source: Responsa Rashba 207, Shulchan Aruch 375:10, Mourning in Halacha pg 158