Is there any special significance when three planets are in conjunction with one another?
I have the sun, mercury, and venus all in conjunction in my 9th house.
http://www.astro.com/tmpd/cvmtfile8NB3jP-u1478480394/astro_w2at_01_michael.46386.4082.gif
Yes, I just referred to that in my response to your earlier post.
Mercury can never be more than 27 degrees from the Sun, Venus no more than 48 degrees. So it's reasonably common to find the three of them in either the same house or the same sign.
Modern Astrology will try to blend the three planets into one meaning but I don't find that all that useful. They do however, influence each other.
In my response to your previous post, I suggested using a simple house system to start with. Whole Sign Houses would put them in the tenth, and that makes them all important. As the MC also lies in Gemini, Mercury has significance for your career and the way in which you act in society.
Traditionally, the Sun overpowers planets that are near it, such as Mercury and Venus, and makes it impossible for them to shine through. However the earliest system of Western Astrology, the Hellenistic approach, allowed planets in their own dignities (in this case Mercury rules Gemini) to be protected from the Sun.
The Sun itself has signification for career and social status - it's the adult you, that which signifies your will and has signification for what the Greeks called
nous, which is still used in English as a slang word for wisdom or understanding - its Greek meaning.It rules your judgement and ability, it is key to your identity.
Mercury rules your rational mind - the ability to think logically and rationally. With both these planets in good condition, and well placed They work well together
Venus is key to relationships and involving others. It give social skills and artistic temperament ane even the extent to which you are exhibitionist, with the desire to wear jewellery etc that you quoted in the previous post. BUT it's the condition by sign and house that indicates how far these become part of you. We all have Venus in our chart but placements in different signs and houses, so we are not all very artistic or very flamboyant or enjoy the good things of lfe to the same extent. Your Venus is not very strong in terms of its sign placement, though the conjunction with Mercury may help you to overcome problems in that area, Venus is also trined by Saturn and sextiled by Mars. These aspects are not strong but both Mars and Saturn bring difficulty. Especially Mars in this chart. Luckily the aspect isn't a square but you may find that letting your Venus side out isn't easy and when you do, you might overdo it.