From a pure mathematical perspective, this is possible. For example, consider dates $t_0 \le t_1 < t_2 < t_3$. Given
\begin{align*}
L(t_0, t_1, t_2) = \frac{1}{\Delta t_2}\left(\frac{P(t_0, t_1)}{P(t_0, t_2)}-1 \right),
\end{align*}
and
\begin{align*}
L(t_0, t_2, t_3) = \frac{1}{\Delta t_3}\left(\frac{P(t_0, t_2)}{P(t_0, t_3)}-1 \right),
\end{align*}
where $\Delta t_i = t_i-t_{i-1}$, and $P(t, u)$ is the price at time $t$ of a zero-coupon bond with maturity $u$ and unit face value.
Then
\begin{align*}
L(t_0, t_1, t_3) &= \frac{1}{t_3-t_1}\left(\frac{P(t_0, t_1)}{P(t_0, t_3)}-1 \right)\\
&=\frac{1}{t_3-t_1}\left(\frac{P(t_0, t_1)}{P(t_0, t_2)}\frac{P(t_0, t_2)}{P(t_0, t_2)}-1 \right)\\
&=\frac{1}{t_3-t_1}\Big(\big(1+\Delta t_2 L(t_0, t_1, t_2)\big)\big(1+\Delta t_3 L(t_0, t_2, t_3) \big)-1 \Big).
\end{align*}
For example, assuming 30 days a month and the day-count convention is 30/360. If FRA $1\times 4$ is 4% and FRA $4\times 7$ is 5%, then
\begin{align*}
FRA \,1\times 7 &=\frac{1}{0.5}\Big(\big(1+0.25\times 0.04)\big)\big(1+0.25 \times 0.05 \big)-1 \Big)\\
&=0.04525,
\end{align*}
that is, 4.525%.