Yes you can do it (and probably should when you understand the purpose of each Scrummy practice), but don't expect to be praised by Scrummers.
I'm extremely happy to discuss the reasons I want to change something, but all to often the only counter-argument is "that isn't Scrum". I'm 100% fine with that, but I'm not going to do something if the only reason for it is religion.
If communication is a problem, having a daily standup just pretends the problem doesn't exist, rather than solve it.
100% this. The only thing a synchronous team-wide meeting is useful for is revealing a significant issue and getting a prompt and definite acknowledgement from the team. And then, if it's a priority, some help with the issue. But given the proper tool, even that feature can be made asynchronous.
It gets worse if the team is actually 2-4 different teams with not much overlap (because companies tend to adopt these agile methodologies without much thought and it just keeps growing and including more people because.. it's nice, right?). Then you're ignoring (or not having a clue) about 90% of the meeting, and it's _daily_.
The daily standup, IMO, should be only to remove impediments, and if you have none, then a sentence or two will suffice. I see the DS as the most useful meeting, as you are aware of what your workmates are doing.
And if Scrum is still a pain in the back, then you have Kanban, which is sort of Scrum without the straitjackets.