Did any of the scholars say that it is permissible to recite two of the opening supplications in prayer?

What appears to be the case from the Sunnah is that the worshipper should recite only one of the opening supplications.

Bukhari (744) and Muslim (597) narrated from Abu Hurayrah (may Allah be pleased with him) that he said: The Messenger of Allah (blessings and peace of Allah be upon him) used to remain silent between the takbir and recitation, and that period of silence was brief. I said: May my father and mother be sacrificed for you, O Messenger of Allah. When you remain silent between the takbir and recitation, what do you say? He said: “I say: Allahumma ba‘id bayni wa bayna khatayaya kama ba‘adta bayna al-mashriqi wa’l-maghrib. Allahumma naqqini min al-khataya kama yunaqqa ath-thawb al-abyad min al-danas. Allahumma ighsil khatayaya bi’l-ma’i wa’th-thalji wa’l-barad (O Allah, put a great distance between me and my sins, as great as the distance You have made between the East and the West. O Allah, cleanse me of sin as a white garment is cleansed from filth. O Allah, wash away my sins with water and snow and hail).”

Shaykh Ibn ‘Uthaymin was asked: Can a person combine two types of the opening supplications?

He (may Allah have mercy on him) replied: He should not combine two types of the opening supplication, because it is soundly narrated in as-Sahihayn that Abu Hurayrah (may Allah be pleased with him) said: … And he quoted the hadith referred to above.

Then he said:

When someone asked the Prophet (blessings and peace of Allah be upon him) what he should say [in the opening supplication], he only told him of one supplication. This indicates that it is not prescribed to combine different types thereof."(Fatawa Ibn ‘Uthaymin  13/122).

Shaykh Ibn Baz (may Allah have mercy on him) said:

The Sunnah is to vary the opening supplication. The Prophet (blessings and peace of Allah be upon him) did not combine them. Sometimes he would recite the opening supplication that is narrated in the hadith of ‘Umar: “Subhanak Allahumma wa bi hamdik, wa tabarak asmuka wa ta‘ala jadduka wa la ilaha ghayruk (glory and praise be to You, O Allah, blessed be Your name, exalted be Your majesty; there is no god worthy of worship except You).” And sometimes he would recite that which is narrated in the hadith of Abu Hurayrah: “Allahumma ba‘id bayni wa bayna khatayaya… (O Allah, put a great distance between me and my sins…),” which is narrated in as-Sahihayn…"( Fatawa Nur ‘ala ad-Darb by Ibn Baz  8/172).

Some of the scholars are of the view that there is nothing wrong with combining opening supplications in a single prayer. It says in al-Mawsu‘ah al-Fiqhiyyah (4/52):

The view of Abu Yusuf, the companion of Abu Hanifah, and of a number of the Shafa‘is, including Abu Ishaq al-Marwazi and al-Qadi Abu Hamid – and it is also the view favoured by al-Wazir ibn Hubayrah, who was one of the companions of Imam Ahmad – is that two of the supplication narrated in the reports may be put together: “Subhanak Allahumma wa bi hamdik… (Glory and praise be to You, O Allah…).” and “Wajjahtu wajhiya… I have set my face towards…).”

An-Nawawi also recommended that the opening supplications should include all the versions that have been narrated, for one who is praying on his own, and for the imam, if those who are praying behind him give him permission to do so. End quote.

Shaykh Muhammad ibn Muhammad al-Mukhtar ash-Shinqiti was asked: Is it permissible to combine the narrated versions of the opening supplication in prayer, or should the worshipper recite only one of them?

He (may Allah preserve him) replied:

The view that was favoured by a number of scholars is that he should vary it, so he should recite one supplication sometimes, and another one sometimes, because the difference here has to do with variation, and the reports do not contradict one another. Based on that, he should vary it, so he may recite one supplication in one prayer, and another supplication in another prayer, because that was the practice of the Messenger of Allah (blessings and peace of Allah be upon him).

But if he combines all of them in one prayer, then there are two scholarly views. The first view is that favoured by Imam an-Nawawi (may Allah have mercy on him), which is that there is nothing wrong with putting these supplications together.

The other view is that favoured by Shaykh al-Islam and others, which is that there is no report which speaks of putting them together; therefore he should limit it only to what was narrated.

What is better and more prudent is for the individual to limit it only to what was narrated, so he should recite one in his prayers sometimes, and recite another one in his prayers sometimes, as was narrated from the Prophet (blessings and peace of Allah be upon him)."(Sharh Zad al-Mustaqni‘ by Shaykh ash-Shinqiti).

And Allah knows best.