In the House of Representatives
As Frank Cedeno said, it would be perfectly legal for the House to repeat whatever pieces of the impeachment process they choose, as many times as they want. The only thing that they (probably) can't do is unimpeach after they've voted on and passed articles of impeachment.
The House can open a new investigation, hold more hearings under the existing one (closed or open), write new reports or add addendums to the previous ones, and/or vote to add new articles to the existing set.
All of this is true regardless of whether the Senate has started to try the President, is in the middle of doing so, or has previously voted to acquit. If they vote to convict and remove the President from office (or the President resigns), the President is no longer impeachable, but everything else is still an option for the House - it might lead to changes to laws, a referral to prosecutors for criminal charges, or just dig up more political dirt.
Since the Democrats currently control the House, where everything can be passed by simple majority, they can do any of these things over any Republican objections (as they have for the whole process). This would include calling Bolton to testify in an open hearing and writing a new article of impeachment based on the result.
In the Senate
In the Senate, on the other hand, the Democrats have very little power (but not as little as the Republicans in the House). The Senate can set whatever rules it wants for the trial, except that the SCOTUS Chief Justice must preside over it and that it takes 2/3 to convict. That leaves a lot of leeway for the Senate to make whatever rules they want, which are all doable by simple majority. This also applies to any other mid-trial decisions (or rule changes) such as whether to call a given witness. (I'm not actually sure if cloture is relevant to impeachment rule changes, but even if it is, there's ways around the 2/3 it'd normally require.)
As such, if the Democrats want to call any witnesses during the trial, they need enough Republicans to vote with them to reach 51 votes to do so.