If you're looking for a private tour from Mumbai to Delhi and Agra to visit the Taj Mahal, there are several options available. Here's a sample itinerary you can consider:

Day 1: Mumbai to Delhi

Start your day early and travel from Mumbai to Delhi
Upon arrival in Delhi, you'll be greeted by a private driver who will transfer you to your hotel.
Spend the rest of the day at leisure, exploring the city or relaxing in your hotel.
Day 2: Delhi Sightseeing

After breakfast, embark on a full-day sightseeing tour of Delhi.
Visit popular attractions like the Red Fort, Jama Masjid, Qutub Minar, India Gate, Humayun's Tomb, and Raj Ghat.
Explore bustling markets like Chandni Chowk and enjoy local street food.
In the evening, return to your hotel and rest.
Day 3: Delhi to Agra

After an early breakfast, check out from your hotel and proceed towards Agra by private car.
Upon arrival in Agra, check in to your hotel and freshen up.
Visit the Agra Fort, a Unesco World Heritage site known for its stunning architecture and historical significance.
Enjoy a mesmerising sunset view of the Taj Mahal from Mehtab Bagh, a garden complex across the river.
Day 4: Taj Mahal and Return to Delhi

Early in the morning, visit the Taj Mahal to witness its beauty during sunrise, considered the best time to appreciate its grandeur.
Spend ample time exploring the Taj Mahal and learning about its history and significance.
Return to your hotel for breakfast and check out.
Afterwards, start your journey back to Delhi.
Upon reaching Delhi, you can either check into a hotel or proceed directly to the airport or railway station for your onward journey.
Please note that this is just a suggested itinerary, and you can customise it based on your preferences and time constraints. It's advisable to make arrangements with a reputable travel agency or tour operator who can assist you in organising a private tour that suits your requirements.