A believer is the brother of a believer, so it is not lawful for a believer to outbid his brother, and he should not propose an engagement when his brother has thus proposed until he gives it up. (Using translation from Muslim 1414)
أَنَّهُ سَمِعَ عُقْبَةَ بْنَ عَامِرٍ عَلَى الْمِنْبَرِ يَقُولُ إِنَّ رَسُولَ اللهِ ﷺ قَالَ الْمُؤْمِنُ أَخُو الْمُؤْمِنِ فَلَا يَحِلُّ لِمُؤْمِنٍ أَنْ يَبْتَاعَ عَلَى بَيْعِ أَخِيهِ حَتَّى يَذَرَ وَلَا يَخْطُبُ عَلَى خِطْبَةِ أَخِيهِ حَتَّى يَذَرَ