In some jurisdictions, e.g. the UK, you can apply for a series mark, which can include multiple versions of your logo. However, these versions should vary only in non-substantial changes, such as one being colourful and one in black-and-white. In the US, submitting only the black-and-white version is sufficient to protect the colourful versions as well.
However, if you have multiple logos, the only way to protect them all would be to file a separate application for each of them. Since this can dramatically increase the cost of registration, we often recommend business owners choose the variation of the logo they use the most.