在AndroidManifest.xml文件中添加以下代码来请求多个权限：

private final int MY_PERMISSIONS_REQUEST_MULTIPLE = 123;

private void requestMultiplePermissions() {
    String[] permissions = {
        Manifest.permission.READ_CONTACTS,
        Manifest.permission.WRITE_CONTACTS,
        Manifest.permission.CAMERA,
        Manifest.permission.ACCESS_FINE_LOCATION
    };

    ArrayList permissionList = new ArrayList<>();
    for (String permission : permissions) {
        if (ContextCompat.checkSelfPermission(this, permission) != PackageManager.PERMISSION_GRANTED) {
            permissionList.add(permission);
        }
    }

    if (!permissionList.isEmpty()) {
        ActivityCompat.requestPermissions(this, permissionList.toArray(new String[permissionList.size()]), MY_PERMISSIONS_REQUEST_MULTIPLE);
    }
}

@Override
public void onRequestPermissionsResult(int requestCode, String[] permissions, int[] grantResults) {
    switch (requestCode) {
        case MY_PERMISSIONS_REQUEST_MULTIPLE: {
            Map perms = new HashMap<>();
            // Initial
            for (String permission : permissions) {
                perms.put(permission, PackageManager.PERMISSION_GRANTED);
            }
            // Fill with results
            for (int i = 0; i < grantResults.length; i++) {
                perms.put(permissions[i], grantResults[i]);
            }
            // Check for all permissions
            boolean allGranted = true;
            for (String permission : permissions) {
                if (perms.get(permission) != PackageManager.PERMISSION_GRANTED) {
                    allGranted = false;
                    break;
                }
            }
            if (allGranted) {
                // All permissions granted
            } else {
                // Permission denied
            }
        }
        break;
    }
}

在需要多个权限的位置调用requestMultiplePermissions()方法即可。在用户请求完所有权限后，onRequestPermissionsResult()方法将被调用。处理所有权限是否被授予的逻辑。