The supplication after the prayer is:
اللهم أنت السلام ومنك السلام تباركت ياذا الجلال والإكرام
Some people add extra words to this supplication like حيِّنا ربنا بِالسَّلام etc which are not recorded from our beloved Prophet صل الله عليه وسلم. Such additions are permissible as supported by the incident mentioned in the books on Hajj whereby Abdullah b. Umar narrated the whole talbiyah of the prophet. He then added the following sentences which are not reported by the prophet صل الله عليه وسلم.
لبيك لبيك وسعديك والخير في يديك لبيك والرغبي اليك
It should however be noted that there is no allowance to make changes in prescribed supplications. The proof for this is the incident where the Prophet صل الله عليه وسلم taught a man a supplication. He memorised it and repeated in front of the Prophet, but changed the words “بنبيك الذي أرسلت” to “برسولك الذي أرسلت”. The Prophet صل الله عليه وسلم didn’t let the change go uncorrected.
In summary, if the addition is to glorify and praise Allah then it is permissible with a caution to not consider it a sunnah[1].
It is confirmed that in the supplication of waseelah after adhaan, the extra words like والدرجة الرفيعة and وارزقنا شفاعته يوم القيامة are not authentically proven from the prophet صل الله عليه وسلم. However, words with similar meaning appeared in other narrations.
Imam Tahaawi[2] recorded from Ibn Mas’ud the supplication with these words:
اللهم اعط محمد الوسيلة وارفع في الاعلين درجته
Ibn ‘Abbas narrated these words[3]:
اللهم صل عليه وبلغه درجة الوسيلةعندك واجعلنا في شفاعته يوم القيامة
Imam al-Bayhaqi[4] included the following:
انك لا تخلف الميعاد
Hence, addition of the like والدرجة الرفيعة and وارزقنا شفاعته يوم القيامة is permissible[5].
[1] Tuhfah vol 2, pg 94
[2] Tahaawi vol 1, pg 87
[3] Kanzul ‘Ummaal vol 7, pg 704
[4] Sunan al-Kubra vol 1, pg 410
[5] Tuhfah vol 1, pg 535