Limited atonement (which really should be renamed 'powerful atonement' or something like that) is often accused of being 'a doctrine without a text'. Whilst this is in many ways a non-argument (who seriously wants to limit 'what the bible teaches' to 'what can be proved from proof texts'?) and Romans 8:32 is a proof-text of sorts, there are also a number of texts that suggest that Jesus' cross-work was undertaken with the specific purpose of saving the elect.
I think Hebrews 2:13-15 is probably one of those sort of texts. It strongly implies the doctrine of limited atonement.
13 And again, "I will put my trust in him." And again, "Behold, I and the children God has given me." 14 Since therefore the children share in flesh and blood, he himself likewise partook of the same things, that through death he might destroy the one who has the power of death, that is, the devil, 15 and deliver all those who through fear of death were subject to lifelong slavery.
vs 13 envisages those who belong to Christ as family members as 'the children' given to him by God. Then vs 14 says that it was because of the humanity of specifically these children that the Son also adopted a human nature (flesh and blood) in order to die a death that rescued them from slavery.
In other words we have atonement explicitly linked with election. Christ's cross-work flowed out of the Father's giving to the Son. It was very definitely 'for us and for our salvation' that the Son was made incarnate and went to his Satan-whupping death.