MudBlazor ChipSet - selecting chips programmatically

I need to implement a "Select all" functionality whereby the user can select all chips via a button click, rather that clicking each item (which can be many!)

<MudButton Variant="Variant.Outlined"            OnClick="(() => AllChips.ToList().ForEach(x => x.IsSelected = true))">    Select all media</MudButton><MudChipSet SelectedChips="@SelectedChips"             MultiSelection="true"             Filter="true">     @foreach (var chip in AllChips)     {<MudChip Text="@chip.Text" />     }</MudChipSet>

I've explored the IsSelected and Default properties of a MudChip to no avail. The tooltip I get is that those properties should not be set outside of their component.

Is this possible to achieve with MudChipSet?