Purity: Multiple Obligatory Ghusls and Tayammum
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 710:
If someone cannot perform ghusl and a few ghusls are obligatory for him, it is permitted for him to perform one tayammum in place of all of them. However, the recommended precaution is that he should perform one tayammum in place of each ghusl.
-Ayatullah Sistani, Practical Laws of Islam, Purification (Taharah)