To make something longer or larger:
* Prolong: (especially of time)
* Enlarge: (to increase in size)
* Expand: (to become greater in size or scope)
* Lengthen: (to make something longer)
* Stretch: (to make something longer or wider)
* Amplify: (to make something greater or stronger)
* Augment: (to increase the size or amount of something)
* Supplement: (to add to something)
To offer something:
* Offer: (to present something for acceptance)
* Grant: (to give something formally)
* Bestow: (to give something as a gift or honor)
* Proffer: (to offer something politely)
* Present: (to formally give something)
To reach out or make contact:
* Reach: (to extend a hand or arm)
* Stretch out: (to extend a limb or body)
* Outstretch: (to extend something outward)
* Contact: (to make connection with)
* Communicate: (to share information or ideas)
To continue or last:
* Last: (to continue for a period of time)
* Continue: (to carry on)
* Persist: (to continue to exist or happen)
* Endure: (to last for a long time)
The best synonym for "extend" will depend on the specific context in which you are using it.