It is not allowed to combine more than two prayers together, and the prayers combined can only be:
- Dhuhr and 'asr, either during the time of dhuhr (taqdīm) or 'asr (ta'khīr), or
- Maghrib and 'ishā', either during the time of maghrib (taqdīm) or 'ishā' (ta'khīr).
The rule is to pray every prayer in its specific time:
إِنَّ الصَّلَاةَ كَانَتْ عَلَى الْمُؤْمِنِينَ كِتَابًا مَّوْقُوتًا
Indeed, prayer has been decreed upon the believers a decree of specified times.
— Surat An-Nisa 4:103
The prayers must be conducted in the manner that the Prophet ﷺ did as per the following hadith narrated by Abu Sulaiman and Malik ibn Huwairith (abridged):
ارْجِعُوا إِلَى أَهْلِيكُمْ فَعَلِّمُوهُمْ وَمُرُوهُمْ، وَصَلُّوا كَمَا رَأَيْتُمُونِي أُصَلِّي، وَإِذَا حَضَرَتِ الصَّلاَةُ فَلْيُؤَذِّنْ لَكُمْ أَحَدُكُمْ، ثُمَّ لِيَؤُمَّكُمْ أَكْبَرُكُمْ
Return to your families and teach them (religious knowledge) and order them (to do good deeds) and offer your prayers in the way you saw me offering my prayers, and when the stated time for the prayer becomes due, then one of you should pronounce its call (i.e. the Adhan), and the eldest of you should lead you in prayer.
— Sahih al-Bukhari, Book 78, Hadith 39
Ibn Taymiyyah in his book Majmū' al-Fatāwa, Vol. 23, pp. 292 said that shortening the prayers from four rak'ahs to two rak'ahs is only permitted while travelling, while combining prayers is permitted due to travelling, weather conditions, or health conditions with the objective being removing hardship (see Sunan an-Nasa'i 1/6/603).
It is, therefore, obvious that the standard is to pray each prayer in its dedicated time, with exemptions being provided under specific conditions. As such, these exemptions can only be done within the frame of what the Prophet ﷺ practiced (said, did, or approved).
There is evidence from the Sunnah that the Prophet ﷺ combined dhuhr and 'asr prayers, e.g., the hadith narrated by Jabir ibn 'Abdullah (abridged):
فَنَزَلَ بِهَا حَتَّى إِذَا زَاغَتِ الشَّمْسُ أَمَرَ بِالْقَصْوَاءِ فَرُحِّلَتْ لَهُ حَتَّى إِذَا انْتَهَى إِلَى بَطْنِ الْوَادِي خَطَبَ النَّاسَ ثُمَّ أَذَّنَ بِلاَلٌ ثُمَّ أَقَامَ فَصَلَّى الظُّهْرَ ثُمَّ أَقَامَ فَصَلَّى الْعَصْرَ وَلَمْ يُصَلِّ بَيْنَهُمَا شَيْئًا
He stayed there until the sun had passed its zenith, then he called for Al-Qaswa' which was saddled for him. When he reached the bottom of the valley he addressed the people. Then Bilal called the Adhan, then the Iqamah, then he prayed Zuhr, then he called the Iqamah, then he prayed 'Asr, and he did not offer any other prayer in between.
— Sunan an-Nasa'i, Vol. 1, Book 6, Hadith 605
There is evidence from the Sunnah that the Prophet ﷺ also combined maghrib and 'ishā' prayers, e.g., the hadith narrated by Usamah ibn Zaid (abridged):
فَرَكِبَ فَلَمَّا جَاءَ الْمُزْدَلِفَةَ نَزَلَ فَتَوَضَّأَ فَأَسْبَغَ الْوُضُوءَ ثُمَّ أُقِيمَتِ الصَّلاَةُ فَصَلَّى الْمَغْرِبَ ثُمَّ أَنَاخَ كُلُّ إِنْسَانٍ بَعِيرَهُ فِي مَنْزِلِهِ ثُمَّ أُقِيمَتِ الْعِشَاءُ فَصَلاَّهَا وَلَمْ يُصَلِّ بَيْنَهُمَا شَيْئًا
He then mounted. When he reached Al Muzdalifah he alighted performed the ablution, performed it well. Thereafter iqamah for the prayer was called and he offered the sunset prayer. Then everyone made his Camel kneel down at his place. Iqamah was then called for night prayer and he offered it but he did not pray between them.
— Sunan Abi Dawud, Book 11, Hadith 205
There is no evidence that the Prophet ﷺ combined prayers in any other manner.