About Levelling CE

Well, it does increases the bonus in HP/ATK that the CE gives to your servant, which is a little nice extra...but not it's special effect. Who is likely what we all actually care about when equipping them.

For this, Limit Break them (feed another CE identical 4 times). This will also increase their max level.

It can be done gradually and probably will be just from all the garbage CEs you'll be getting from the FP gacha