Can we use any other titles or honorifics other than Mr, Ms or Mrs before a person's name if we don't want to express their gender?
Sometimes a role or qualification has an honorific:
Mx and Misc are documented as possible gender neutral titles, but I cannot recall them being used in any document I've seen.
Often you may either use the full name of the person or just the family name.
In our recent correspondence Anna Gable ...
There are no commonly-used gender-neutral honorifics in English at the current time. Many have been suggested, but none have been sufficiently adopted that the average speaker will recognize them. Using these will, at best, only cause confusion.
If the person has a military rank, you may use that (e.g. General Powell). Other jobs have similar honorifics like Captain (of a marine vessel or aircraft), Judge, Doctor (either medical or academic), Senator, President, Minister, Bishop, etc.
Otherwise the convention is to use the person's full name. Of course, some names are themselves gender-neutral -- Morgan, Jamie, Cory, etc. -- but then it's up to the reader to decide if the gender is important.
[Edit] Related article: Me, Myself, and Mx. (from 2015) which suggests that the honorific Mx. may be more common in the UK than the US. It's certainly not common in the US, although language is fluid so who knows? However, if you are writing to a group of people familiar with gender-neutral pronouns then it's only polite to adopt their language.
Otherwise, again, it's unlikely the average person will understand what you are trying to say. Also, many have strong feelings about the entire issue of gender, so unless you intend to incite a debate, it's best to avoid using these honorifics as they may distract from what you are trying to say.
As others have noted, there are no commonly-accepted gender-neutral honorifics in English. I do, however, remember reading a science fiction novel where all important persons, or persons in formal situations, were referred to as "M. LastName," a gender-neutral version of Mr., Mrs., and Ms., similar to Mx. and pronounced simply as "em."
While the other answers pretty much covered it, since this is ELL, an important aspect of practical usage is that non-professional titles/honorifics are on the way out. There are still plenty of places where you'll find they're requested (official forms, online account creation forms, etc.), sometimes as a thinly-veiled proxy for asking gender, and still plenty of lines of work where you're expected to be able to use them with clients/customers/partners/etc., but younger generation native speakers largely do not use them, and find their use weird and awkward.
For a non-native speaker trying to navigate an English-speaking environment, I think the most important piece of advice about using these honorifics/titles is: don't. Unless you're in a situation where social protocols call for it and you're not comfortable bending them.