Multiple experiments may be run concurrently on a website. However, as with any standard A/B or multivariate testing platform, there are considerations to be aware of.
Ascend will allow a site visitor to participate in only one experiment at a time. This is fine so long as your site has enough traffic to support the segregation of visitors, and the experiments don't "cross funnels", e.g. single page conversion funnels.
There may be cases where two business groups, say one tasked with optimizing the home page, and another tasked with optimizing product detail pages to checkout, want to run their own experiments at the same time. This can be done, but the decision to do so must be made knowing that the two experiments may throttle one another and distort the type of traffic that enters them.
In the homepage and PDP scenario, any user entering a site at the homepage would be placed into the homepage experiment, effectively throttling the PDP experiment, slowing down its progression to completion. Surely the PDP pages would receive traffic from people that search for a product on Google, or click on paid media ads, social, content and email marketing, effectively bypassing the home page, but the population of the PDP experiment is then effectively distorted to not reflect behaviors of the the true, whole population of site traffic. This may or may not materially affect an experiment's outcomes. It depends on the nature of the website, its traffic, and its conversions.
As a guiding principle, it's preferable to not run concurrent experiments whose funnels cross paths. Rather, they should be run serially, one after the other. This also has the benefit of allowing each experiment to receive as much traffic and conversions as possible in order to speed the process. However, Ascend does not prevent one from doing so, given that one is informed of how experiment outcomes may be affected.