Otherwise to answer the initial question, in a word...no. The cellular towers, along with the mobile phone itself determine the next best cell tower to move to, first by the mobile phone identifying and securing an open channel on a tower with stronger signal, then the towers together command the phone to switch channels, while at the same time the towers themselves switch channels from the one on the fading tower to the one on the stronger one. There is nothing you at the phone level can do to prevent or promote switching from one tower to another except to either move farther away from the less desirable tower and closer to the more desirable tower, or to somehow block the signal from the less desirable tower and collect/enhance/increase the signal from the more desirable tower.
The latter can actually effectively be done by creating a metal shield blocking the phone's antenna from the direction of the less desirable tower, and at the same time, use that or another supplemental shield to collect and reflect the more desirable tower's signal to the phone's antenna. You would look pretty geeky walking around with a metal shield held up behind the phone but it can actually work. In a more appropriate fashion, a "repeater" antenna can be placed on the roof with a directional "Yagi" antenna pointing at the more desirable tower, and then either a passive (cable to another internal antenna), or active (signal booster/amplifier), antenna system can be installed interior to the building that will "repeat" the more desirable signal inside and being that the more desirable signal could/would be significantly stronger than the less desirable one, the phone and towers would (hopefully) negotiate the carrier signal to be transferred to the more desirable tower. You can "force" this transition if the less desirable tower already holds the signal by switching the radio off and on (airplane mode, for instance), and in all liklihood the phone and towers will opt for the stronger signal when re-establishing the cellular connection.
There is still no assurance that the tower with the stronger signal will be chosen, since there is the potential for the stronger tower to have all channels occupied at that moment, whereas the less desirable tower might have open channels. There is really no assurance that any one tower will be used all the time, but statistically the system will negotiate to the tower with the stronger signal if given the opportunity both to reduce consumption of power at the cell site (tower transmitter) and also from the phone.
