If a muslim is trying to solve some problem or has an important or pressing business like that of trying to reconcile between two people or parties and he fears that if he left them there and went for prayer, the people will disperse and will not come to reconciliation then in such a case there is no blame on him if he delays offering prayer in congregation with the first congregation and prayes with the congregation aftre that or he prayes by himself if he is unable to join any congregation. That is a valid excuse for not offering the prayer in congregation or delaying it.
Al-Bukhaari (2690) and Muslim (421) narrated from Sahl ibn Sa‘d (may Allah be pleased with him) that there was a dispute among some people from Banu ‘Amr ibn ‘Awf, so the Messenger of Allah (blessings and peace of Allah be upon him) went out to them, with some of his companions, to bring about reconciliation among them. The time for prayer came, but the Prophet (blessings and peace of Allah be upon him) did not come [to the mosque]. Bilaal came and gave the call to prayer, but the Prophet (blessings and peace of Allah be upon him) did not come. So Bilaal went to Abu Bakr and said: The Prophet (blessings and peace of Allah be upon him) has been detained (by some matter) and it is time to pray; will you come and lead the people in prayer? He said: Yes, if you wish. So he gave the iqaamah (the call immediately preceding the prayer), and Abu Bakr went forward (to lead the people in prayer) …
If the prayer is one that can be joined to the prayer that comes after it, such as Zuhr, which may be joined with ‘Asr, or Maghrib, which may be joined with ‘Isha’, then it may be joined with the later prayer, and there is nothing wrong with delaying it and praying the two prayers together.
Accorsing to sunnah it is permissible to put the two prayers together if one has some pressing buainess that cannot be left or delayed or if one is in a situation that renders him unable to pray at the time of prayer, even if one is at home.
Ibn Rajab al-Hanbali (may Allah have mercy on him) said:
Ahmad stated that it is permissible to put two prayers together in the event of being engaged in some pressing business.
It was narrated from Ibn Sireen: There is nothing wrong with putting two prayers together when there is a need to do so, so long as that is not taken as a habit. End quote.
As for delaying prayer until its time has ended without putting it together with the following prayer, if the two prayers can be put together, that is not permissible.
A person must strive to offer the prayer on time without delaying it but if the matter is as such that cannot be delayed then in that case a person can forgo praying in congregation and offer prayer in some other congregation or all by himself.
And Allah knows best.