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 wudoo’, then prays two rak‘ahs intending them as the Sunnah prayer of Fajr, the Sunnah prayer following wudoo’ 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 fard (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.
End quote from al-Majmoo‘ (1/325).
Al-Ghazaali said in Ihyaa’ ‘Uloom ad-Deen (4/370-371):
Acts of obedience and worship are connected to their intentions, as far as their soundness is concerned and so 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, so for each intention he will have a reward. 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:
1.. 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.”
2.. Waiting for one prayer after another.
3.. Spending some time in devotion, by restraining his hearing, sight and physical faculties from moving and wandering, for i‘tikaaf is restraint and it is akin to fasting, which is a type of devotion.
4.. 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.
5.. Focusing on remembering Allah, or listening to that which will remind him of Allah.
6.. 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.
7.. Getting to know brothers in faith.
8.. 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 hasanaat (rewards for good deeds) will multiply. End quote.
Shaykh Ibn Baaz (may Allah have mercy on him) said:
A person may do wudoo’ and pray two rak‘ahs, intending them to be the Sunnah prayer following wudoo’, but if he enters the mosque after doing wudoo’ and prays two rak‘ahs, intending them to be greeting the mosque and the Sunnah prayer following wudoo’, he will attain two rewards: the reward of the Sunnah prayer following wudoo’ 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 Zuhr, meaning that he does wudoo’, enters the mosque, and intends the Sunnah prayer of Zuhr, the Sunnah prayer following wudoo’ and the Sunnah prayer of greeting the mosque, he will attain the reward of all of that, praise be to Allah.
End quote from Fataawa Noor ‘ala ad-Darb (11/57).
And Allah knows best.