Is Reward Multiplied For Multiple Intentions in a Single Deed?
Question

Is the reward multiplied if there are multiple intentions for the same action, such as if a person prays two Sunnah Rak`ahs of Fajr, intending thereby to seek the reward for that and the reward for the Sunnah prayer following Wudu and the reward for “greeting the mosque” (Tahiyyat Al-masjid)?
Praise be to Allah.Yes, the reward may be multiplied if there are multiple intentions for a single deed. If the Muslim enters the mosque having done Wudu, then prays two rak`ahs intending them as the Sunnah prayer of Fajr , the Sunnah prayer following Wudu and the Sunnah prayer of greeting the mosque , he will attain the reward of what he intended, and Allah is the bestower of great bounty.
An-Nawawi (may Allah have mercy on him) said:
“If a person starts to pray, intending it as both the obligatory prayer and the prayer to greet the mosque, his prayer is valid and he will attain the reward of both the obligatory prayer and greeting the mosque." (Al-Majmu`  1/325)
Al-Ghazali (may Allah have mercy on him) said in Ihya’ `Ulum Ad-Din (4/370-371):
“Acts of obedience and worship are connected to their intentions, as far as their soundness is concerned and as far as their multiple reward is concerned .
With regard to soundness, it means that he intends by doing this action to worship Allah, may He be Exalted, and nothing else; if he intends to show off, then his action becomes a sin.
With regard to multiple reward , that is connected to the number of good intentions. By doing one act of obedience and worship, it is possible to intend many good things thereby, and he will have a reward for each intention. That is because for each of these intentions he will have a reward, and each reward will be multiplied tenfold, as is mentioned in the Hadith. 
For example, sitting in the mosque is an act of worship, and a person may have several intentions when doing that, so that it becomes like one of the good deeds of the pious, and he attains thereby the level of those who are close to Allah.
Whilst sitting in the mosque, he may do the following:

Believing that (the mosque) is the House of Allah, and that the one who enters it is visiting his Lord, so he intends thereby to visit his Lord in the hope of what the Messenger of Allah (blessings and peace of Allah be upon him) promised when he said: “Whoever sits in the mosque has visited Allah, may He be Exalted, and it is incumbent upon the one who is visited to honour his visitor.”
Waiting for one prayer after another.
Spending some time in devotion, by restraining his hearing, sight and physical faculties from moving and wandering, for I`tikaf is restraint and it is akin to fasting, which is a type of devotion.
Focusing one’s thoughts on Allah and reflecting upon the hereafter, and warding off everything that may distract him from that by staying in the mosque.
Focusing on remembering Allah, or listening to that which will remind him of Allah.
Intending to benefit others with his knowledge by enjoining what is right and forbidding what is wrong, because in the mosque there are bound to be people who pray badly or engage in activities that are not permissible in the mosque.
Getting to know brothers in faith.
Refraining from sins out of shyness before Allah, may He be Exalted, and out of shyness lest one do in the house of Allah that which is a transgression against its sanctity.

This is a way to increase the number of intentions, and you can extend this by analogy to all other acts of worship and permissible actions, because there is no act of obedience and worship that cannot have several intentions. The believer may bring to mind intentions commensurate with his eagerness to do good and his efforts to do that. Thus, his deeds will grow and his rewards for good deeds will multiply .” 
Shaykh Ibn Baz (may Allah have mercy on him) said:
“A person may do Wudu and pray two Rak`ahs, intending them to be the Sunnah prayer following Wudu, but if he enters the mosque after doing Wudu and prays two Rak`ahs, intending them to be greeting the mosque and the Sunnah prayer following Wudu, he will attain two rewards: the reward of the Sunnah prayer following Wudu and the reward of greeting the mosque. Praise be to Allah, the bounty of Allah is immense. If he prays with the intention of offering the regular Sunnah prayer of Dhuhr, meaning that he does Wudu, enters the mosque, and intends the Sunnah prayer of Dhuhr , the Sunnah prayer following Wudu and the Sunnah prayer of greeting the mosque, he will attain the reward of all of that, praise be to Allah." (Fatawa Nur `Ala Ad-Darb  11/57)
And Allah knows best.