Is polite te form exists?

So for ichidan verbs like taberu, the te form is tabete and the polite te form is tabemashite? Is it really a thing? And can it be further conjugated, e.g polite negative te form?

Also what would be the polite te form of godan verbs like kiku? kiite is the non polite, but kikimashite would ignore te form rules.. so kiimashite?

Thanks!

by Dxceuz