Du`a for New Clothes
Question

It was narrated from the Prophet (blessings and peace of Allah be upon him) that he used to offer supplication when putting on his clothes. Should the individual offer supplication when putting on each piece of clothing, or is it sufficient to offer supplication once for everything that he puts on?
Praise be to Allah.Du`a when wearing clothes
The hadiths which speak of the dhikr that is recommended (mustahabb) when putting on clothes are of two types:

The first type is hadiths which mention the specific dhikr that is recommended when putting on a new garment:

Abu Sa‘id al-Khudri (may Allah be pleased with him) said:
When the Messenger of Allah (blessings and peace of Allah be upon him) put on a new garment, he would mention it by name, whether it was a chemise or a turban, then he would say: “Allahumma laka al-hamd, anta kasawtanihi, as-aluka min khayrihi wa khayri ma suni‘a lah, wa a'udhu bika min sharrihi wa sharri ma suni‘a lah  (O Allah, to You be praise, You have clothed me with it. I ask you for its good and the good of that for which it was made, and I seek refuge in You from its evil and the evil of that for which it was made).” (Narrated by Abu Dawud (no. 4023); classed as sahih by Ibn al-Qayyim in Zad al-Ma'ad (2/345), and by al-Albani in Sahih Abi Dawud.)

The second type is hadiths which are general in meaning, and the recommendation of reciting dhikr is not limited to putting on new clothes only; rather it may be recited when putting on any garment:

Mu‘adh ibn Anas narrated that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever puts on a garment and says: ‘Al-hamdu Lillah illadhi kasani hadha’th-thawba wa razaqanihi min ghayri hawlin minni wa la quwwah (Praise be to Allah Who has given me this garment to wear and has provided it for me with no strength or power on my part),’ will be forgiven his past and future sins.” (Narrated by Abu Dawud (no. 4023); classed as sahih by Ibn Hajar in al-Khisal al-Mukaffirah (74), and by al-Albani in Sahih Abi Dawud, apart from the phrase “and future sins.” Al-Bayhaqi included this hadith in a chapter in Shu‘ab al-Iman (8/307) entitled: Section on what one should say when putting on a garment. This is general and is not limited to putting on new clothes only.)
Moreover, in some books which quote the hadith, there is an addition which specifies “a new garment.” It is most likely that this is an addition that was not originally part of the hadith. We have checked most of the original books which narrated this hadith, and this specification is not mentioned in them.
Scholars’ views on du’a for new clothes
Based on this variation in the hadiths, the scholars differentiated between these two dhikrs. So they stated that:

The first dhikr – “Allahumma laka al-hamd, anta kasawtanihi, as-aluka min khayrihi wa khayri ma suni‘a lah, wa a'udhu bika min sharrihi wa sharri ma suni‘a lah  (O Allah, to You be praise, You have clothed me with it. I ask you for its good and the good of that for which it was made, and I seek refuge in You from its evil and the evil of that for which it was made).” – is to be recited when putting on a new garment.
The second dhikr – “Al-hamdu Lillah illadhi kasani hadha’th-thawba wa razaqanihi min ghayri hawlin minni wa la quwwah (Praise be to Allah Who has given me this garment to wear and has provided it for me with no strength or power on my part)” – is to be recited when putting on any garment, whether it is old or new.

This seems to be the way in which Imam an-Nawawi listed the hadith in al-Adhkar (p. 20-21).
He stated that clearly elsewhere, as he (may Allah have mercy on him) said:
The Sunnah is to say, when putting on a garment: “Al-hamdu Lillah illadhi kasani hadha’th-thawba wa razaqanihi min ghayri hawlin minni wa la quwwah (Praise be to Allah Who has given me this garment to wear and has provided it for me with no strength or power on my part).” And when he puts on a new garment, he should say: “Allahumma anta kasawtanihi, as-aluka khayrahu wa khayra ma suni‘a lah, wa a'udhu bika min sharrihi wa sharri ma suni‘a lah  (O Allah, You have clothed me with it. I ask you for its good and the good of that for which it was made, and I seek refuge in You from its evil and the evil of that for which it was made).”(Al-Majmu‘  4/647).
This version was adopted in some contemporary books of adhkar, such as Hisn al-Muslim (Fortress of the Muslim).
However, the way in which some scholars introduce this dhikr in their books is in reference to putting on a new garment only.
See: Sunan ad-Darimi (2/378); there is something similar in al-Wabil as-Sayyib (226), where it says:
Section on the dhikr which a person should recite or which may be recited to him  when he puts on a new garment. See also Kashshaf al-Qina‘ (1/288).
Repeating du`a when putting on several pieces of clothing
With regard to the question about repeating this dhikr when putting on several pieces of clothing, the matter is flexible, in sha Allah, although what is more likely to be the case, in our view, is that it may be said once for all the items of clothing.
For more about making du`a at certain occasions, please see these answers: 20176 , 121254 , 2355 , and 69759  
And Allah knows best.