Moyes has recently signed Russian winger Diniyar Bilyaletdinov, but has also lost Joleon Lescott in a big-money move to Manchester City.
“I would be disappointed if we didn’t get at least four, maybe more,” Moyes told Everton’s official website.
“We’ve made quite a bit of progress I feel and maybe I’ll be able to announce something shortly, but not yet.
“The job is to try and make it (the squad) stronger every year and that’s what we’ll aim to do.”
