Select All mat option and deselect All

Simply you can do it without adding a new option to your data source by adding a checkbox.

See the: Demo

import { Component, VERSION, ViewChild } from '@angular/core';
import { FormControl } from '@angular/forms';
import { MatSelect } from '@angular/material/select';
import { MatOption } from '@angular/material/core';

@Component({
  selector: 'my-app',
  templateUrl: './app.component.html',
  styleUrls: [ './app.component.css' ]
})
export class AppComponent  {
  @ViewChild('select') select: MatSelect;

  allSelected=false;
   foods: any[] = [
    {value: 'steak-0', viewValue: 'Steak'},
    {value: 'pizza-1', viewValue: 'Pizza'},
    {value: 'tacos-2', viewValue: 'Tacos'}
  ];
  toggleAllSelection() {
    if (this.allSelected) {
      this.select.options.forEach((item: MatOption) => item.select());
    } else {
      this.select.options.forEach((item: MatOption) => item.deselect());
    }
  }
   optionClick() {
    let newStatus = true;
    this.select.options.forEach((item: MatOption) => {
      if (!item.selected) {
        newStatus = false;
      }
    });
    this.allSelected = newStatus;
  }
}

.select-all{
  margin: 5px 17px;
} 

<mat-form-field>
  <mat-label>Favorite food</mat-label>
  <mat-select  #select multiple>
    <div class="select-all">
        <mat-checkbox [(ngModel)]="allSelected"
                        [ngModelOptions]="{standalone: true}"
                        (change)="toggleAllSelection()">Select All</mat-checkbox>
    </div>
    <mat-option (click)="optionClick()" *ngFor="let food of foods" [value]="food.value">
      {{food.viewValue}}
    </mat-option>
  </mat-select>
</mat-form-field>

Here is an example of how to extend a material option component.

See stackblitz Demo

Component:

import { ChangeDetectorRef, Component, ElementRef, HostListener, HostBinding, Inject, Input, OnDestroy, OnInit, Optional } from '@angular/core';
import { MAT_OPTION_PARENT_COMPONENT, MatOptgroup, MatOption, MatOptionParentComponent } from '@angular/material/core';
import { AbstractControl } from '@angular/forms';
import { MatPseudoCheckboxState } from '@angular/material/core/selection/pseudo-checkbox/pseudo-checkbox';
import { Subject } from 'rxjs';
import { takeUntil } from 'rxjs/operators';

@Component({
  selector: 'app-select-all-option',
  templateUrl: './select-all-option.component.html',
  styleUrls: ['./select-all-option.component.css']
})
export class SelectAllOptionComponent extends MatOption implements OnInit, OnDestroy {
  protected unsubscribe: Subject<any>;

  @Input() control: AbstractControl;
  @Input() title: string;
  @Input() values: any[] = [];

  @HostBinding('class') cssClass = 'mat-option';

  @HostListener('click') toggleSelection(): void {
    this. _selectViaInteraction();

    this.control.setValue(this.selected ? this.values : []);
  }

  constructor(elementRef: ElementRef<HTMLElement>,
              changeDetectorRef: ChangeDetectorRef,
              @Optional() @Inject(MAT_OPTION_PARENT_COMPONENT) parent: MatOptionParentComponent,
              @Optional() group: MatOptgroup) {
    super(elementRef, changeDetectorRef, parent, group);

    this.title = 'Select All';
  }

  ngOnInit(): void {
    this.unsubscribe = new Subject<any>();

    this.refresh();

    this.control.valueChanges
      .pipe(takeUntil(this.unsubscribe))
      .subscribe(() => {
        this.refresh();
      });
  }

  ngOnDestroy(): void {
    super.ngOnDestroy();

    this.unsubscribe.next();
    this.unsubscribe.complete();
  }

  get selectedItemsCount(): number {
    return this.control && Array.isArray(this.control.value) ? this.control.value.filter(el => el !== null).length : 0;
  }

  get selectedAll(): boolean {
    return this.selectedItemsCount === this.values.length;
  }

  get selectedPartially(): boolean {
    const selectedItemsCount = this.selectedItemsCount;

    return selectedItemsCount > 0 && selectedItemsCount < this.values.length;
  }

  get checkboxState(): MatPseudoCheckboxState {
    let state: MatPseudoCheckboxState = 'unchecked';

    if (this.selectedAll) {
      state = 'checked';
    } else if (this.selectedPartially) {
      state = 'indeterminate';
    }

    return state;
  }

  refresh(): void {
    if (this.selectedItemsCount > 0) {
      this.select();
    } else {
      this.deselect();
    }
  }
}

HTML:

<mat-pseudo-checkbox class="mat-option-pseudo-checkbox"
                     [state]="checkboxState"
                     [disabled]="disabled"
                     [ngClass]="selected ? 'bg-accent': ''">
</mat-pseudo-checkbox>

<span class="mat-option-text">
  {{title}}
</span>

<div class="mat-option-ripple" mat-ripple
     [matRippleTrigger]="_getHostElement()"
     [matRippleDisabled]="disabled || disableRipple">
</div>

CSS:

.bg-accent {
  background-color: #2196f3 !important;
}

Use code as below create function on click each mat-option and select()/deselect() all option:

See stackblitz:https://stackblitz.com/edit/angular-material-with-angular-v5-jsgvx6?file=app/app.component.html

TS:

togglePerOne(all){ 
   if (this.allSelected.selected) {  
    this.allSelected.deselect();
    return false;
}
  if(this.searchUserForm.controls.userType.value.length==this.userTypeFilters.length)
    this.allSelected.select();

}
  toggleAllSelection() {
    if (this.allSelected.selected) {
      this.searchUserForm.controls.userType
        .patchValue([...this.userTypeFilters.map(item => item.key), 0]);
    } else {
      this.searchUserForm.controls.userType.patchValue([]);
    }
  }

HTML:

<form [formGroup]="searchUserForm" fxFlex fxLayout="column" autocomplete="off" style="margin: 30px">
    <mat-select placeholder="User Type" formControlName="userType" multiple>
        <mat-option *ngFor="let filters of userTypeFilters" [value]="filters.key" (click)="togglePerOne(allSelected.viewValue)">
            {{filters.value}}
        </mat-option>
        <mat-option #allSelected (click)="toggleAllSelection()" [value]="0">All</mat-option>
    </mat-select>
</form>

Another way to do this is with the @ViewChild selector to get the mat-select component and troggle the mat-options items selected or unselected. We need also a variable to save the selected actual status to select or unselect all the elements on every click. Hope will help.

  import {MatOption, MatSelect} from "@angular/material";
  
  export class ExampleAllSelector {
  
    myFormControl = new FormControl();
    elements: any[] = [];

    allSelected = false;

    @ViewChild('mySel') skillSel: MatSelect;

    constructor() {}

    toggleAllSelection() {
      this.allSelected = !this.allSelected;  // to control select-unselect
      
      if (this.allSelected) {
        this.skillSel.options.forEach( (item : MatOption) => item.select());
      } else {
        this.skillSel.options.forEach( (item : MatOption) => {item.deselect()});
      }
      this.skillSel.close();
    }
  }

      <mat-select #mySel placeholder="Example" [formControl]="myFormControl" multiple>
        <mat-option [value]="0" (click)="toggleAllSelection()">All items</mat-option>
        <mat-option *ngFor="let element of elements" [value]="element">{{skill.name}}</mat-option>
      </mat-select>