Doing more than one khatm of Qur’aan at the same time
Question

Is it permissible for me to start more than one khatm at the same time, without finishing the first khatm? i.e., I start the second one and the first one together, and end them together. May Allah reward you with good.
Praise be to Allah.The Holy Qur’aan is the Word of Allah, and reading it is one of the best acts of worship and dearest of the actions that bring a person close to Allah. The more a Muslim reads it, the greater the reward he attains. 
It was narrated from ‘Abd-Allah ibn Mas‘ood (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: 
“Whoever reads one letter of the Book of Allah will have one hasanah, and the reward for one hasanah is ten like it. I do not say that ‘Alif, laam, meem’ is one letter, but ‘Alif’ is a letter, ‘laam’ is a letter and ‘meem’ is a letter.” 
Narrated by al-Tirmidhi (2910); he said: it is hasan saheeh ghareeb with this isnaad. It was classed as saheeh by al-Albaani in Saheeh al-Tirmidhi. 
This reward is attained by the one who reads any soorah of the Qur’aan, whether it is during a complete reading (khatm) in which the soorahs are read in order, or in his prayer, or when reading Qur’aan randomly without paying attention to a specific khatm.  
But it is better to let one’s khatm be in sequence, from the beginning of the Qur’aan to the end, reading the soorahs in the Mushaf in order, and not to start another khatm until he has reached the end of the one that he started before that. This is the practice of the Salaf (early generations) in this matter, and this is what recommended, to complete the Qur’aan in one month or less.  
He should not go against that and start another khatm unless there is a reason for that, such as if he wants to complete the Qur’aan in prayer and has another khatm (complete reading) outside of prayer, or he is completing it once from the Mushaf and once from memory, or he has one khatm in which is reads quickly, focusing more on tilaawah (recitation) and another in which he is focusing on pondering and understanding the meaning, and he does not mind whether he reads a lot or a little, and so on. 
There may be the worry that if a person starts another khatm for no good reason, that this may be due to haste and a lack of patience in that he does not read the Mushaf to the end, in addition to the fact that this is contrary to what is known of the practice of the Salaf. 
For more information on the practice of the Salaf with regard to completing the Qur’aan (khatm al-Qur’aan), please see al-Tibyaan fi Adaab Hamalat al-Qur’aan by Imam al-Nawawi (may Allah have mercy on him), 75-82. 
And Allah knows best.