No
You cannot include GNU Affero GPL v3.0 or later code in a BSD 3-Clause License-licensed project and ship the result under BSD 3-Clause License. GNU Affero GPL v3.0 or later requires the combined work to be distributed under GNU Affero GPL v3.0 or later (or compatible). If your project is meant to stay BSD 3-Clause License-only, do not include GNU Affero GPL v3.0 or later code in it.
| License | Family | Patent grant |
|---|---|---|
| GNU Affero GPL v3.0 or later (AGPL-3.0-or-later) | network-copyleft | Yes |
| BSD 3-Clause License (BSD-3-Clause) | permissive | No (implicit at most) |
GNU Affero GPL v3.0 or later: AGPL-3.0 with explicit upgrade path.
BSD 3-Clause License: Three-clause BSD: like 2-clause plus a no-endorsement clause.
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