Q:

How to add anchor support to a core block?

I want to add anchor (id) support to a core block. I tried the JS code below in the editor to alter the cover block. It correctly adds the anchor field under Advanced properties; however reloading the edit page results in the This Block Contains Unexpected or Invalid Content error. 
What additional hooks do I need? Is this possible to do in an easy/elegant way?
function addBlockAnchor( settings, name ) {
    if ( name !== 'core/cover' ) {
        return settings;
    }

    return lodash.assign( {}, settings, {
        supports: lodash.assign( {}, settings.supports, {
            anchor: true
        } ),
    } );
}
wp.hooks.addFilter(
    'blocks.registerBlockType',
    'my-plugin/addBlockAnchor',
    addBlockAnchor
);

My final code with @niklas answer:
function addBlockAnchor( settings, name ) {
    if ( name !== 'core/cover' ) {
        return settings;
    }

    lodash.assign( settings, settings, {
        supports: lodash.assign( {}, settings.supports, {
            anchor: true
        } ),
        attributes: lodash.assign( {}, settings.attributes, {
            anchor: { type: 'string' }
        } ),

    } );

    return settings;
}

wp.hooks.addFilter(
    'blocks.registerBlockType',
    'norpel-blocks/addBlockAnchor',
    addBlockAnchor
);

A:

You will also have to add an anchor attribute to the blocks attributes like so. Not tested, but it should work.
const addBlockAnchor = props => {
  if (props.attributes) { // Some blocks don't have attributes
    props.attributes = {
      ...props.attributes,
      anchor: {
        type: 'string'
      }
    }
  }
  return props
}

wp.hooks.addFilter(
  'blocks.registerBlockType',
  'namespace/with-anchor',
  addBlockAnchor
)

