I'd like one more blanket, please.

Literal

Blanket [object-を] one-more blanket-counter [want-ほしいのですが].

The polite want-frame ほしいのですが ('I want X… [is that OK?]') — an extremely common way to softly request something. The trailing が is the dangling softener. もう一枚 ('one more [flat object]') uses the counter 枚 for thin, flat things (blankets, sheets, paper, plates).