I would not support that, here's why.
In 1929 then Secretary of State Henry Stimson said that "gentlemen don't read each other's mail." Fast forward to WWII and you have Alan Turing and the British guys trying to break the
enigma machine, which Eisenhower said was "decisive" in an Allied Victory.
Around this time,
OSS was training agents using a handbook from British Intelligence. The first OSS officers were trained in Canada. This is an example of how the US cooperated with its allies to develop new intelligence. Notice how the US was completely deficient in its intelligence before adopting the MI6 model for intelligence gathering methods and assassination. This expanded the global pool of military recruits from which the Allies could draw intelligence agents.
Since the advent of the CIA in 1947, the US has expanded it's use of intelligence on a global scale. According to a 2013
article, the CIA expanded it's budget and recently surpassed any other agency in the intelligence community. While it is not the role of the CIA to collect data on US Citizens, having foreign allies here adds depth to the intelligence community. It is not out of the question that the CIA would be motivated to share information around military programs with foreign intelligence, such as information regarding members of foreign armed services on US soil. In short, we don't need further militarization of the CIA.
I think, in principle, it's a great idea to share resources with allies. However, the military which regularly interacts with locals in communities around the US has had a profound impact. So called
"military communities" around military bases house transient members of the armed services who travel among bases. Military families are a symptom of the militarization of our culture in a nationalistic sense. Adding ally bases would further militarize our culture right here in America. I don't support that because the military presence is strong enough.
I have nothing against our allies, and I think that our best work is done when we share operators. Our best interest may not be installing bases to receive a certain nationality of ally in each case. Instead, the use of translators on our own soil can accommodate allies. After WWII, we made sure to maintain and expand our military presence overseas. The MI6 "investment" paid off. I think we should cease expansion of foreign military operations now that our diplomacy is valued, although sometimes questioned, like in the case of Snowden. We have business relations to uphold. Why jeopardize that with more military bases?