Transwarp Beaming
Originally postulated by Starfleet officer Montgomery Scott, Transwarp Beaming is an almost entirely theoretical process in which one is able to beam onto a ship at warp. This is a difficult, dangerous process. To quote Montgomery Scott, "The notion of transwarp beaming is like trying to hit a bullet with a smaller bullet whilst wearing a blindfold, riding a horse." This is, of course, an extreme simplification, but it is a more than adequate metaphor.
It is achieved by using a transporter pad's subspace compensator to 're-energize' a ship's warp trail, creating a brief, tumultuous tunnel of extremely compressed subspace in which one can attempt to beam something or someone onto a ship traveling at Warp. This is limited to ships travelling at speeds below warp seven; any faster and it becomes too dangerous.
There are a number of things that can go wrong with such an attempt, mostly pertaining to the difficulties encountered beaming within a warp bubble. This makes up the 'blindfolded' portion of the metaphor. Within a warp bubble, any attempt at transporting to a specific location is limited to a vague, 'best guess' scenario. Within a starship, this can be fatally insufficient. A subject could accidentally be transported into a wall or bulkhead, or worse, outside of a ship but within its' warp bubble. Such a subject would then quickly fall 'out' of the ship's warp bubble, and be torn apart at a molecular level by the intense gravitational forces.
Moreover, advances in warp technology have effectively made this impossible, at least onboard federation ships. For one, Federation warp drives are shielded against transwarp beaming attempts; they essentially 'harden' themselves during an entry attempt. Additionally, Federation transporter pads have safeguards built in to prevent such attempts (affectionately called 'moron-shielding' by some engineers) because of the risk involved. Even prior to these advances, attempts at transwarp beaming were extremely rare, because of the risk involved.
// Note: This is mostly just an attempt to make JJTrek's Transwarp Beaming make any sense, any sense at all. It has no bearing on any RP. Unless, of course, you want to integrate it into your RP. But this is mostly my brain going: This DON'T MAKE SENSE, FIX ITTT.