All perfect praise be to Allah, The Lord of The Worlds. May His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
The ruling depends on whether they are held simultaneously or consecutively, in addition to the condition of the mosque itself. If the congregations are held consecutively, then this isn`t disliked particularly if the mosque is often-visited, such as that of the market`s. However, if the congregations are held simultaneously, this is disliked according to the majority of the scholars.
If the appointed Imam was late, it is recommended to wait for him and it isn`t permissible to hold the congregational prayer without him especially if this is expected to cause division. However, if he was too late, then it is permissible to hold the prayer without him provided that division isn`t expected to happen, but if it is then each should offer their prayer individually.
The Shafie scholar Ibn Hajar (May Allah have mercy on him) said: "It is disliked to hold congregational prayer in a non-often-visited mosque that has an appointed Imam without the permission of the latter, whether before, after or at the same time he is leading the congregation. If he was late, then it is recommended to wait for him. However, if he was too late, then it is permissible to hold the prayer without him provided that division isn`t expected to happen, but if it is then each should offer their prayer individually." {Tohfat Al-Mohtaj, Vol.2: 253}.
In conclusion, in principle, one congregation should be held for the same prayer in the mosque, which isn`t often visited but has an appointed Imam, especially if division is expected. Therefore, a Muslim should be keen on avoiding disliked acts accompanying congregational prayer so as not to miss its reward. However, it is permissible to hold multiple congregations in the often-visited mosques, even if they have an appointed Imam, or those that have no Imam. And Allah the Almighty knows best.