rivalverb
Society women are ever endeavouring to outrival their neighbour in social splendour.
Their rich colour, grace, and forms outrivalled in beauty all other creatures.
These figures are staggering, yet they are far outrivalled by the great department store in Chicago.

SMART Vocabulary: related words and phrases

Competing and contending (non-sporting)
as a dare
be one up on someoneidiom
cat
catchup
challenge someone to something/do something
dare
get one up on someoneidiom
give someone/something a run for their moneyidiom
go in for something
go toe to toeidiom
hyper-competitive
jungle
pit
sharp elbowsidiom
sharp-elbowed
sharpen (something) up
sharpen your elbowsidiom
showing
snap
toe