If your editorial agreement(s) do not attempt to prevent editors from starting or participating in a new journal, then your editorial board might seek to launch an alternative journal.
The first step in developing an alternative journal is to develop an editorial prospectus for the new journal. With this in hand, your editorial board for the prospective journal might approach relevant partners to determine whether one or more might be willing to sponsor the journal, in full or in part, and to support the new journal within an existing publication workflow.
Such publishing solutions will often expect the editorial operation to support itself financially. This might require your editorial group to assess whether you are willing to support the journal through volunteer labor, or whether some level of paid support might be required. If the latter, your editorial board—perhaps with the assistance of the publishing platform host—will need to identify potential funding sources for the editorial operation.