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Wrong duplicate in the comment, but the answer is yes. That is how a multiple-entry visa is supposed to work, to save both you and the consulates the paperwork.
- You must have days left on the duration. If no shorter duration is given, you can stay up to 90 days out of every 180 days. If a shorter total duration is given, this applies. Note that fractional days count full.
- You must plan to leave the Schengen area again.
- You must be able to afford your stay and bring enough money or means to pay. The amount per day is different for each Schengen country.