Good points by others, but if you decide to bore it, yes you can go .060 over. .060 over on a 350 would be 4.060, and a small block 400 bore is 4.125, although the 400's suffered from overheating issues.
Geoff
1955 2nd Series 3600 235 cid, 4 sp. - Current 1979 Chevy K10 350 cid 4 sp -Sold 1955 2nd Series Wide Window 283 cid 3 sp - Totaled