How would you counsel a menopausal woman with prior provoked VTE on HRT about testosterone supplementation?

Prior VTE was not related to estrogen use, and is not currently on anticoagulation for current transdermal estrogen after risk/benefit discussion. In this scenario, would the addition of testosterone for symtomatic control (energy, libido) favor anticoagulation to reduce thrombotic risk? Would you counsel her against it given the risks and potential limited benefits?